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  • Articles  (105)
  • 06A10  (82)
  • Wetlands
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  • 1985-1989  (105)
  • Mathematics  (83)
  • Energy, Environment Protection, Nuclear Power Engineering  (22)
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  • Articles  (105)
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  • 1
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    Springer
    Order 2 (1985), S. 193-198 
    ISSN: 1572-9273
    Keywords: 06A10 ; 06D99 ; 52A25 ; Finite distributive lattices ; finite posets ; valuations ; convex polytopes ; extreme points
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let L be a finite distributive lattice and V(L) the real vector space of all valuations on L. We verify the conjecture of Geissinger that the extreme points of the convex polytope M(L)={v ∈ L : 0 ≤ v ≤ 1} are precisely the 0–1 valuations.
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  • 2
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    Order 2 (1985), S. 257-264 
    ISSN: 1572-9273
    Keywords: 06A10 ; 68E05 ; Sorting ; merging ; linear extension
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For a finite poset P and x, yεP let pr(x〉y) be the fraction of linear extensions which put x above y. N. Linial has shown that for posets of width 2 there is always a pair x, y with 1/3 ⩽ pr(x〉y)⩽2/3. The disjoint union C 1∪C 2 of a 1-element chain with a 2-element chain shows that the bound 1/3 cannot be further increased. In this paper the extreme case is characterized: If P is a poset of width 2 then the bound 1/3 is exact iff P is an ordinal sum of C 1∪C 2's and C 1's.
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  • 3
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    Order 3 (1986), S. 283-286 
    ISSN: 1572-9273
    Keywords: 06A10 ; 06A12 ; 06B99 ; Partially ordered set ; semilattice ; lattice ; cofinality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A partial ordering on a set P can be weakened to an upper or lower semilattice ordering, respectively a lattice ordering, if and only if P is filtered in the appropriate direction(s).
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  • 4
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    Order 3 (1987), S. 355-357 
    ISSN: 1572-9273
    Keywords: 05App ; 06A10 ; Factor poset ; antichain ; depth
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Denote g(m, n) the minimum of min A, where A is a subset of {1, 2, ..., m} of size n and there do not exist two distinct x and y in A such that x divides y. We use a method of poset to prove that g(m, n)=2 i for positive integer i≤log3 m and 1+s(m, i−1)〈n≤1+s(m, i), where s(m, i) is the number of odd integers x such that m/3 i 〈x≤m.
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  • 5
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    Order 4 (1987), S. 127-142 
    ISSN: 1572-9273
    Keywords: 06A10 ; 68-XX ; Poset ; closures ; Hasse diagram
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The combinatorial properties of the poset of closures are studied, especially the degrees in the Hasse diagram.
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  • 6
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    Order 3 (1986), S. 1-2 
    ISSN: 1572-9273
    Keywords: 06A10 ; Jump number
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    Topics: Mathematics
    Notes: Abstract The following result is proved in this note: For any positive integers w and t, if an ordered set P has jump number at least (t+1) w−1, then either the width of P is more than w, or P has a tower, i.e., a linear sum of pairs of noncomparable elements, of height more than t.
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  • 7
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    Order 4 (1987), S. 155-164 
    ISSN: 1572-9273
    Keywords: 05C55 ; 06A10 ; 62J ; Regressions ; Ramsey theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A regressive function (also called a regression or contractive mapping) on a partial order P is a function σ mapping P to itself such that σ(x)≤x. A monotone k-chain for σ is a k-chain on which σ is order-preserving; i.e., a chain x 1〈...〈xksuch that σ(x 1)≤...≤σ(xk). Let P nbe the poset of integer intervals {i, i+1, ..., m} contained in {1, 2, ..., n}, ordered by inclusion. Let f(k) be the least value of n such that every regression on P nhas a monotone k+1-chain, let t(x,j) be defined by t(x, 0)=1 and t(x,j)=x t(x,j−1). Then f(k) exists for all k (originally proved by D. White), and t(2,k) 〈 f(K) 〈t(е + εk, k) , where εk → 0 as k→∞. Alternatively, the largest k such that every regression on P nis guaranteed to have a monotone k-chain lies between lg*(n) and lg*(n)−2, inclusive, where lg*(n) is the number of appliations of logarithm base 2 required to reduce n to a negative number. Analogous results hold for choice functions, which are regressions in which every element is mapped to a minimal element.
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  • 8
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    Order 4 (1987), S. 269-272 
    ISSN: 1572-9273
    Keywords: 06A10 ; 05A15 ; Interval order ; enumeration
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An algorithm is obtained for enumerating the interval orders of a given cardinality.
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  • 9
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    Order 3 (1987), S. 345-353 
    ISSN: 1572-9273
    Keywords: 06A10 ; 06A23 ; Order-dimension ; Ferrers relation ; partition lattice ; linear lattice
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The aim of this paper is to study the order-dimension of partition lattices and linear lattices. Our investigations were motivated by a question due to Bill Sands: For a lattice L, does dim L=n always imply |L|≥2 n ? We will answer this question in the negative since both classes of lattices mentioned above form counterexamples. In the case of the partition lattices, we will determine the dimension up to an absolute constant. For the linear lattice over GF(2), L n , we determine the dimension up to a factor C/n for an absolute constant C.
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  • 10
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    Order 3 (1987), S. 369-382 
    ISSN: 1572-9273
    Keywords: 06A10 ; Partial order ; tree ; chain decomposition ; width
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We establish some inequalities connecting natural parameters of a partial order P. For example, if every interval [a,b] contains at most λ maximal chains, if some antichain has cardinality v, and if there are χ1 chains whose union is cofinal and coinitial in P, then the chain decomposition number for P is ⩽χ1λv (Theorem 2.2), and the inequality is sharp in a certain sense (Section 3).
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  • 11
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    Order 4 (1987), S. 37-42 
    ISSN: 1572-9273
    Keywords: 06A10 ; Partially ordered sets ; Van der Waerden's arithmetic sequence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Van der Waerden's arithmetic sequence theorem—in particular, the ‘density version’ of Szemerédi—is generalized to partially ordered sets in the following manner. Let w and t be fixed positive integers and ε〉0. Then for every sufficiently large partially ordered set P of width at most w, every subset S of P satisfying |S|≥ε|P| contains a chain a 1, a 2,..., a 1 such that the cardinality of the interval [a i, a i+1] in P is the same for each i.
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  • 12
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    Order 5 (1988), S. 163-171 
    ISSN: 1572-9273
    Keywords: 05C45 ; 05C70 ; 06A10 ; Boolean lattice ; Hamiltonian cycle ; matching
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract New classes of explicit matchings for the bipartite graph ℬ(k) consisting of the middle two levels of the Boolean lattice on 2k+1 elements are constructed and counted. This research is part of an ongoing effort to show that ℬ(k) is Hamiltonian.
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  • 13
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    Order 6 (1989), S. 59-68 
    ISSN: 1572-9273
    Keywords: 06A10 ; Poset ; minimal cutset ; chain complete ; special points ; regular posets ; Menger's theorem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract If P is a poset, the associated PT-order is the quasi order ⊴ in which a ⊴ b holds if every maximal chain of P which passes through a also passes through b. P is special if whenever A is a chain in P and a=sup A or inf A, then there is b ∈ A such that b ⊴ a. It is proved that if P is chain complete and special then the set of ⊴-maximal elements is ⊴-dominating and contains a minimal cutset. As corollaries of this, we give partial answers to (i) a question of Rival and Zaguia by showing that if P is regular and special every element is in a minimal cutset and (ii) a question of Brochet and Pouzet by showing that if P is chain complete and special then it has the Menger property.
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  • 14
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    Order 1 (1985), S. 235-247 
    ISSN: 1572-9273
    Keywords: 06A10 ; Chain ; antichain ; cutset
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A subset A of an ordered set P is a cutset if each maximal chain of P meets A; if, in addition, A is an antichain call it an antichain cutset. Our principal result is a characterization, by means of a ‘forbidden configuration’, of those finite ordered sets, which can be expressed as the union of antichain cutsets.
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  • 15
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    Order 1 (1985), S. 317-331 
    ISSN: 1572-9273
    Keywords: 06A10 ; 60C05 ; Partially ordered set ; probabilistic methods ; dimension
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Letk andn be positive integers and fix a setS of cardinalityn; letP k (n) be the (partial) order onS given by the intersection ofk randomly and independently chosen linear orders onS. We begin study of the basic parameters ofP k (n) (e.g., height, width, number of extremal elements) for fixedk and largen. Our object is to illustrate some techniques for dealing with these ‘random orders’ and to lay the groundwork for future research, hoping that they will be found to have useful properties not obtainable by known constructions.
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  • 16
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    Order 1 (1985), S. 371-375 
    ISSN: 1572-9273
    Keywords: 06A10 ; Poset ; chain ; antichain ; cutset
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract It is shown that ifP is a poset containing noN, then every minimal cutset inP is an antichain, that the converse also holds whenP is finite, and that this converse fails in general.
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  • 17
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    Order 2 (1985), S. 25-40 
    ISSN: 1572-9273
    Keywords: 06A10 ; 05C20 ; 05C38 ; Order ; diagram ; graph ; orientation ; cycle
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We study some equivalent and necessary conditions for a finite graph to be the covering graph of a (partially) ordered set. For each κ≥1, M. Aigner and G. Prins have introduced a notion of a vertex colouring, here called κ-good colouring, such that a 1-good colouring is the usual concept and graphs that have a 2-good colouring are precisely covering graphs. We present some inequalities for the corresponding chromatic numbers χκ, especially for x 2. There exist graphs that satisfy these inequalities for κ=2 but are not covering graphs. We show also that x 2 cannot be bounded by a function of x=x 1. A construction of Nešetřil and Rödl is used to show that x 2 is not bounded by a function of the girth.
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  • 18
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    Order 2 (1985), S. 387-402 
    ISSN: 1572-9273
    Keywords: 06A10 ; Poset ; linear extension ; correlation ; universal correlation ; Graham, Yao, and Yao inequality ; xyz inequality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Posets $$A,{\text{ }}B \subseteq X{\text{ x }}X$$ are said to be correlated with respect to another poset R on X (we write A↑ R B) if P(R∪A) P(R∪B)≤P(R∪A∪B) P(R). Here P(S) is the probability that a randomly chosen bijection from X to the totally ordered set with |X| elements is a linear extension of S. We study triples (A, B, R) such that A ↑ R B holds for all extensions S of R (we write A $$\begin{array}{*{20}c} \uparrow \\ \uparrow \\ \end{array}$$ R B). Two well-known correlation inequalities, the xyz inequality and an inequality of Graham, Yao, and Yao, can be considered as giving cases when this relation holds. We show when the Graham, Yao, and Yao inequality holds strictly. Our main result is a classification of all R such that (a, b) $$\begin{array}{*{20}c} \uparrow \\ \uparrow \\ \end{array}$$ R (c, d) holds, where a, b, c, d are elements of X.
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  • 19
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    Order 3 (1986), S. 15-20 
    ISSN: 1572-9273
    Keywords: 06A10 ; Partially ordered set
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let P be a partially ordered set. Define k = k (P) = max p∈ |{x ∈ P : p 〈 x or p = x}|, i.e., every element is comparable with at most k others. Here it is proven that there exists a constant c (c 〈 50) such that dim P 〈 ck(log k)2. This improves an earlier result of Rödl and Trotter (dim P ≤2 k 2+2). Our proof is nonconstructive, depending in part on Lovász' local lemma.
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  • 20
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    Order 2 (1985), S. 269-274 
    ISSN: 1572-9273
    Keywords: 06A10 ; Partial order ; fixed point ; comparability graph
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    Topics: Mathematics
    Notes: Abstract We show that the fixed point property is comparability invariant for finite ordered sets; that is, if P and Q are finite ordered sets with isomorphic comparability graphs, then P has the fixed point property if and only if Q does. In the process we give a characterization of comparability invariants which can also be used to give shorter proofs of some known results.
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  • 21
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    Order 5 (1988), S. 21-22 
    ISSN: 1572-9273
    Keywords: 06A10 ; Dimension ; width ; chain-covering number
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    Topics: Mathematics
    Notes: Abstract A partially ordered set with no infinite antichains may have arbitrarily large dimension.
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  • 22
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    Order 3 (1986), S. 21-38 
    ISSN: 1572-9273
    Keywords: 06A10 ; Ladder ; cutset ; 2-cutset property ; chain ; antichain
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An ordered set P is said to have the 2-cutset property if for every element x of P there is a subset S of P whose elements are noncomparable to x, such that |S|≤2 and such that every maximal chain in P meets {x}∪S. It is shown that if P has the 2-cutset property and has width n then P contains a ladder of length [1/2(n−3)].
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  • 23
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    Order 4 (1988), S. 315-318 
    ISSN: 1572-9273
    Keywords: 06A10 ; Circle containment order ; poset
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A partially ordered set is called acircle containment order provided one can assign to each element of the poset a circle in the plane so thatx≤y iff the circle assigned tox is contained in the circle assigned toy. It has been conjectured that every finite three-dimensional partially ordered set is a circle containment order. We show that the infinite three dimensional posetZ 3 isnot a circle containment order.
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  • 24
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    Order 5 (1988), S. 173-186 
    ISSN: 1572-9273
    Keywords: 06A10 ; Ordered set ; retract ; variety ; obstruction
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We use the technique of ‘χ-Embeddings’ to study retracts and varieties of ordered sets. We investigate the class of all ordered sets $$Q$$ which are retract of every ordered set in which $$Q$$ is ‘χ-Embedded’.
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  • 25
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    Order 5 (1989), S. 369-380 
    ISSN: 1572-9273
    Keywords: 06A10 ; Poset ; linear extension ; semiorder ; 1/3–2/3 conjecture ; partially ordered set
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A well-known conjecture of Fredman is that, for every finite partially ordered set (X, 〈) which is not a chain, there is a pair of elements x, y such that P(x〈y), the proportion of linear extensions of (X, 〈) with x below y, lies between 1/3 and 2/3. In this paper, we prove the conjecture in the special case when (X, 〈) is a semiorder. A property we call 2-separation appears to be crucial, and we classify all locally finite 2-separated posets of bounded width.
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  • 26
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    Order 6 (1989), S. 31-37 
    ISSN: 1572-9273
    Keywords: 05A05 ; 06A10 ; Cutset ; Boolean lattice
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    Topics: Mathematics
    Notes: Abstract An informative new proof is given for the theorem of Nowakowski that determines for all n and k the minimum size of a cutset for an element A with |A|=k of the Boolean algebra B n of all subsets of {1,...,n}, ordered by inclusion. An inequality is obtained for cutsets for A that is reminiscent of Lubell's inequality for antichains in B n. A new result that is provided by this approach is a list of all minimum cutsets for A.
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  • 27
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    Order 5 (1989), S. 349-361 
    ISSN: 1572-9273
    Keywords: 05C10 ; 06A10 ; Convex Hasse representations ; Kuratowski type results for Hasse diagrams
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A plane Hasse representation of an acyclic oriented graph is a drawing of the graph in the Euclidean plane such that all arcs are straight-line segments directed upwards and such that no two arcs cross. We characterize completely those oriented graphs which have a plane Hasse representation such that all faces are bounded by convex polygons. From this we derive the Hasse representation analogue, due to Kelly and Rival of Fary's theorem on straight-line representations of planar graphs and the Kuratowski type theorem of Platt for acyclic oriented graphs with only one source and one sink. Finally, we describe completely those acyclic oriented graphs which have a vertex dominating all other vertices and which have no plane Hasse representation, a problem posed by Trotter.
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  • 28
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    Order 6 (1989), S. 265-275 
    ISSN: 1572-9273
    Keywords: 05C75 ; O5C99 ; 06A10 ; Upper bound graph ; multigraph ; poset ; chordal graph ; interval graph
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    Topics: Mathematics
    Notes: Abstract The study of upper bound graphs of posets can be extended naturally to multigraphs. This paper characterizes such upper bound multigraphs, shows they determine the associated posets up to isomorphism, and extends results of D. Scott to characterize posets having chordal or interval upper bound multigraphs.
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  • 29
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    Order 5 (1988), S. 235-237 
    ISSN: 1572-9273
    Keywords: 06A10 ; Circle containment order ; poset
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    Topics: Mathematics
    Notes: Abstract A partially ordered set P is called a circle containment order provided one can assign to each x∈P a circle C x so that $$x \leqslant y \Leftrightarrow C_x \subseteq C_y $$ . We show that the infinite three-dimensional poset N 3 is not a circle containment order and note that it is still unknown whether or not [n]3 is such an order for arbitrarily large n.
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  • 30
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    Order 6 (1989), S. 1-14 
    ISSN: 1572-9273
    Keywords: 06A10 ; Fixed point ; irreducible element ; dismantlability ; cutset ; retraction ; crown
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    Topics: Mathematics
    Notes: Abstract There exist exactly eleven (up to isomorphism and duality) ordered sets of size ≤10 with the fixed point property and containing no irreducible elements.
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  • 31
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    Order 6 (1989), S. 39-47 
    ISSN: 1572-9273
    Keywords: 06A10 ; Inclusion orders ; circle orders ; angle orders
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    Topics: Mathematics
    Notes: Abstract A poset is a circle order if its points can be mapped into circular disks in the plane so that x〈y in the poset precisely when x's circular disk is properly included in y's; the poset is an angle order if its points can be mapped into unbounded angular regions that preserve 〈 by proper inclusion. It is well known that many finite angle orders are not circle orders, but has been open as to whether every finite circle order is an angle order. This paper proves that there are finite circle orders that are not angle orders.
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  • 32
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    Order 6 (1989), S. 91-99 
    ISSN: 1572-9273
    Keywords: 08A40 ; 06A10 ; Clones ; crowns ; tences ; generators
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    Topics: Mathematics
    Notes: Abstract In this paper we study the clones of all order preserving operations for crowns and fences. By presenting explicit generating sets, we show that these clones are finitely generated. The case of crowns is particularly interesting because they admit no order preserving near unanimity operations. Various related questions are also discussed. For example, we give a new proof of a theorem of Duffus and Rival which states that crowns are irreducible.
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  • 33
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    Order 6 (1989), S. 235-240 
    ISSN: 1572-9273
    Keywords: 06A10 ; 52A37 ; Order ; sphere ; partially ordered set ; space-time
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    Topics: Mathematics
    Notes: Abstract Ann-sphere order is a finite partially ordered set representable by containment ofn-spheres in Euclidean (n+1)-space. We present a sequence {P i } of ordered sets such that eachP i is ann-sphere order only forn≥i; one consequence is that we are able to determine the dimension of a Euclidean space-time manifold from the finite suborders of its causality order.
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  • 34
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    Order 2 (1985), S. 165-171 
    ISSN: 1572-9273
    Keywords: 06A10 ; 60C05 ; Partially ordered set ; diameter ; random structures
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    Topics: Mathematics
    Notes: Abstract Let P k (n) be the (partial) order determined by intersecting k random linear orderings of a set of size n; equivalently, let P k (n) consist of n points chosen randomly and independently from the unit cube in ℝ k , with the induced product order. We show for each fixed k〉1, that with probability approaching 1 as n→∞, the comparability graph of P k (n) is connected and has diameter 3.
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  • 35
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    Order 2 (1985), S. 129-144 
    ISSN: 1572-9273
    Keywords: 06A10 ; Poset ; linear extension ; correlation ; universal correlation ; Winkler's Theorem ; universal negative correlation
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    Topics: Mathematics
    Notes: Abstract Posets A, B⫇X×X, with X finite, are said to be universally correlated (A↑B) if, for all posets R over X, (i.e., all posets R⫇Y×Y with X⫇Y), we have P(R∪A) P(R∪B)≤P(R∪A∪B) P(R). Here P(R∪A), for instance, is the probability that a randomly chosen bijection from Y to the totally ordered set with |Y| elements is a linear extension of R∪A. We show that A↑B iff, for all posets R over X, P(R∪A) P(R∪B)≤P(R∪A∪B) P(R∪(A∩B)). Winkler proved a theorem giving a necessary and sufficient condition for A↑B. We suggest an alteration to his proof, and give another condition equivalent to A↑B. Daykin defined the pair (A, B) to be universally negatively correlated (A B) if, for all posets R over X, P(R∪A) P(R∪B)≥P(R∪A∪B) P(R∪(A∩B)). He suggested a condition for A↓B. We give a counterexample to that conjecture, and establish the correct condition. We write A↓B if, for all posets R over X, P(R∪A) P(R∪B)≥P(R∪A∪B) P(R). We give a necessary and sufficient condition for A↓B. We also give constructive techniques for listing all pairs (A, B) satisfying each of the relations A↑B, A↓B, and A↓B.
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    Order 2 (1985), S. 321-322 
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    Keywords: 06A10 ; 05C99 ; Covering graph ; order orientation ; extremal problems
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    Notes: Abstract Every graph G may be transformed into a covering graph either by deletion of edges or by subdivision. Let Π E (G) and Π V (G) denote corresponding minimal numbers. We prove Π E (G) = Π V (G) for every graph G.
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    Order 2 (1985), S. 1-8 
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    Keywords: 06A10 ; Poset ; N-free poset ; linear extension ; Jump number ; matroid ; greedy algorithm ; Rado-Edmonds theorem
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    Notes: Abstract Let L=x 1 x 2...x n be a linear extension of a poset P. Each pair (x i , x i+1) such that x i ≮ x i+1in P is called a jump of L. It is well known that for N-free posets a natural ‘greedy’ procedure constructing linear extensions yields a linear extension with a minimum number of jumps. We show that there is a matroid corresponding to any N-free poset and apply the Rado-Edmonds Theorem to obtain another proof of this result.
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    Order 2 (1985), S. 61-67 
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    Keywords: 06A10 ; Ordered set ; multifunction ; fixed point ; chain-completeness
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    Notes: Abstract Sufficient conditions for the fixed point property for products of two partially ordered sets are proved. These conditions are formulated in terms of multifunctions (functions with non-empty sets as values).
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    Order 2 (1985), S. 119-122 
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    Keywords: 06A10 ; 68C25 ; Chordal bipartite graph ; elimination scheme ; crown
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    Notes: Abstract We prove that a bipartite graph is chordal if and only if it has an elimination scheme. This leads to a polynomial algorithm to recognize whether an ordered set is cycle-free.
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    Order 2 (1985), S. 145-164 
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    Keywords: 06A05 ; 06A10 ; Ordered sets ; linear extension ; greedy dimensions
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    Notes: Abstract Every linear extension L: [x 1〈x 2〈...〈x m ] of an ordered set P on m points arises from the simple algorithm: For each i with 0≤i〈m, choose x i+1 as a minimal element of P−{x j :j≤i}. A linear extension is said to be greedy, if we also require that x i+1 covers x i in P whenever possible. The greedy dimension of an ordered set is defined as the minimum number of greedy linear extensions of P whose intersection is P. In this paper, we develop several inequalities bounding the greedy dimension of P as a function of other parameters of P. We show that the greedy dimension of P does not exceed the width of P. If A is an antichain in P and |P−A|≥2, we show that the greedy dimension of P does not exceed |P−A|. As a consequence, the greedy dimension of P does not exceed |P|/2 when |P|≥4. If the width of P−A is n and n≥2, we show that the greedy dimension of P does not exceed n 2+n. If A is the set of minimal elements of P, then this inequality can be strengthened to 2n−1. If A is the set of maximal elements, then the inequality can be further strengthened to n+1. Examples are presented to show that each of these inequalities is best possible.
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    Order 2 (1985), S. 243-248 
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    Keywords: 06A10 ; Ordered set ; chain ; antichain ; width ; cutset
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    Notes: Abstract The partially ordered set P is an (α, β, γ) ordered set if the width of P≥α, the length of any chain of P≤β and the cut-set number ≤γ. We will prove that if P is an (α, β, γ) ordered set then P contains a ‘simple’ (α, β, γ) ordered set and use this result to prove that if P has the 3 cutset property, then width of P ≤ length of P+3.
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    Order 3 (1986), S. 245-255 
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    Keywords: 06A10 ; 60C05 ; Poset ; diagram ; covering graph ; random graph
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    Topics: Mathematics
    Notes: Abstract For a graph G, we define c(G) to be the minimal number of edges we must delete in order to make G into a covering graph of some poset. We prove that, if p=n -1+η(n) ,where η(n) is bounded away from 0, then there is a constant k 0〉0 such that, for a.e. G p , c(G p )≥k 0 n 1+η(n) .In other words, to make G p into a covering graph, we must almost surely delete a positive constant proportion of the edges. On the other hand, if p=n -1+η(n) , where η(n)→0, thenc(G p )=o(n 1+η(n) ), almost surely.
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    Order 5 (1988), S. 245-255 
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    Keywords: 05C55 ; 05C70 ; 06A10 ; Decomposition ; Ramsey theory ; graph ; finite set system ; partially ordered set ; monotone sequence ; Δ-system ; chain ; antichain ; sub-k coloring
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    Notes: Abstract Every partially ordered set P on at least (1+o(1))n 3 elements can be decomposed into subposets of size n that are ‘almost’ chains or antichains. This lower bound on P is asymptotically best possible. Similar results are presented for other types of combinatorial structures.
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    Order 5 (1988), S. 305-315 
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    Keywords: 06A10 ; Ordered set ; maximal chain ; cutset ; Menger's theorem
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    Notes: Abstract It is shown that, if an ordered set P contains at most k pairwise disjoint maximal chains, where k is finite, then every finite family of maximal chains in P has a cutset of size at most k. As a corollary of this, we obtain the following Menger-type result that, if in addition, P contains k pairwise disjoint complete maximal chains, then the whole family, M (P), of maximal chains in P has a cutset of size k. We also give a direct proof of this result. We give an example of an ordered set P in which every maximal chain is complete, P does not contain infinitely many pairwise disjoint maximal chains (but arbitrarily large finite families of pairwise disjoint maximal chains), and yet M (P) does not have a cutset of size 〈x, where x is any given (infinite) cardinal. This shows that the finiteness of k in the above corollary is essential and disproves a conjecture of Zaguia.
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    Order 5 (1989), S. 345-348 
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    Keywords: 06A10 ; 68C15 ; Preemptive scheduling ; interval order
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    Notes: Abstract In 1979, Papadimitriou and Yannakakis gave a polynomial time algorithm for the scheduling of jobs requiring unit completion times when the precedence constraints form an interval order. The authors solve here the corresponding problem, for preemptive scheduling (a job can be interrupted to work on more important tasks, and completed at a later time, subject to the usual scheduling constraints.) The m-machine preemptive scheduling problem is shown to have a polynomial algorithm, for both unit time and variable execution times as well, when the precedence constraints are given by an interval order.
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    Order 6 (1989), S. 245-263 
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    Keywords: 06A10 ; 68E05 ; Bipartite graph ; Bruhat order ; elementary operations
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    Notes: Abstract Consider two partially ordered setsP, Q and a number of edges connecting some of the points ofP with some of the points ofQ. This yields a bipartite graph. Some pairs of the edges may cross each other because their endpoints atP andQ are oppositely ordered. A natural decrossing operation is to exchange the endpoints of these edges incident atQ, say. This is called a switch. A left lift of an edge means to replace its starting point atP by a larger starting point. A right lift is defined symmetrically for the endpoints atQ. The operation of adding an edge cannot, informally, be explained better. Assume we are given two bipartite graphs π, σ on the node setPσQ. We show that for certain pairs (P, Q) of finite posets, a neat necessary and sufficient criterion can be given in order that σ is obtainable from π by the sequence of elementary operations just defined. A recent characterization of the Bruhat order of the symmetric group follows as a special case.
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    Order 2 (1985), S. 9-23 
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    Keywords: 06A10 ; 68C25 ; Jump number ; substitution decomposition
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    Notes: Abstract Consider the linear extensions of a partial order. A jump occurs in a linear extension if two consecutive elements are unrelated in the partial order. The jump number problem is to find a linear extension of the ordered set which contains the smallest possible number of jumps. We discuss a decomposition approach for this problem from an algorithmic point of view. Based on this some new classes of partial orders are identified, for which the problem is polynomially solvable.
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    Order 2 (1985), S. 199-210 
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    Keywords: 06A10 ; 06A23 ; Poset ; lower end ; directed ; ideal ; chain ; well-ordered ; extension ; completion ; recycling map ; union complete
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    Notes: Abstract A standard extension for a poset P is a system Q of lower ends (‘descending subsets’) of P containing all principal ideals of P. An isomorphism ϕ between P and Q is called recycling if ∪ϕ[Y]∈Q for all Y∈Q. The existence of such an isomorphism has rather restrictive consequences for the system Q in question. For example, if Q contains all lower ends generated by chains then a recycling isomorphism between P and Q forces Q to be precisely the system of all principal ideals. For certain standard extensions Q, it turns out that every isomorphism between P and Q (if there is any) must be recycling. Our results include the well-known fact that a poset cannot be isomorphic to the system of all lower ends, as well as the fact that a poset is isomorphic to the system of all ideals (i.e., directed lower ends) only if every ideal is principal.
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    Order 2 (1985), S. 249-255 
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    Keywords: 06A10 ; 68C25 ; Partially ordered set (poset) ; antichain ; dual transportation problem
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    Notes: Abstract For any finite partially ordered set S we display a dual transportation system of linear inequalities, and a bijection A(x) from the maximal integer-valued solutions x of this system onto the ‘maximal sequences’ of k antichains in S. This provides a simple translation to a dual transportation problem of the problem: find a maximum weight union of k antichains.
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    Order 2 (1985), S. 367-385 
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    Keywords: 06A10 ; 06B99 ; 06C10 ; Geometric lattice ; matroid ; strong map ; shellable ; Möbius function
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    Notes: Abstract We define geometric semilattices, a generalization of geometric lattices. The poset of independent sets of a matroid is another example. We prove several axiomatic and constructive characterizations, for example: geometric semilattices are those semilattices obtained by removing a principal filter from a geometric lattice. We also show that all geometric semilattices are shellable, unifying and extending several previous results.
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    Order 3 (1986), S. 135-153 
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    Keywords: 05C20 ; 05C38 ; 06A10 ; Graph ; orientation ; circuit ; maximal vertex ; pushing down ; order ; diagram
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    Notes: Abstract We study the operation of pushing down elements in the diagram of a finite ordered set. Two natural questions about this operation are, ‘Which orientations of the underlying graph can be obtained from a given orientation by pushing down?’ and ‘Which sets of vertices can become the sets of maximal elements in such orientations?’. For both questions thére are easy necessary conditions. We show that these conditions are also sufficient. The results are extended to cover all induced subgraphs and arbitrary orientations of a finite graph.
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    Order 3 (1986), S. 227-234 
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    Keywords: 06A10 ; Jump number ; tower number
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    Notes: Abstract The maximum jump number of ordered sets having width w and tower number t, denoted by s(w, t), satisfies $$c_l tw\lg w \leqslant s\left( {w,t} \right) \leqslant tw\lg w$$ for some positive constants c 1 and c 2. Specifically, we can obtain c 1=1/8 and c 2〈11/10. When w and t are sufficiently large and w is a power of 2, then $$\left( {\frac{1}{2} - \varepsilon } \right)tw\lg w \leqslant s\left( {w,t} \right) 〈 \frac{7}{{10}}tw\lg w$$ This gives an answer to a problem posed by W. T. Trotter ([3], Problem 15).
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    Order 3 (1986), S. 269-281 
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    Keywords: 05C75 ; 05C99 ; 06A10 ; Poset ; subposet ; m-subposet ; upper bound graph ; graph ; subgraph ; induced subgraph ; digraph
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    Notes: Abstract Competition graphs of transitive acyclic digraphs are strict upper bound graphs. This paper characterizes those posets, which can be considered transitive acyclic digraphs, which have upper bound graphs that are interval graphs. The results proved here may shed some light on the open question of those digraphs which have interval competition graphs.
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    Order 3 (1987), S. 321-330 
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    Keywords: 06A10 ; Poset ; diagram ; NP-completeness
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    Notes: Abstract A diagram is an undirected graph corresponding to the covering relation of a finite poset. We prove that three decision problems related to diagrams are NP-complete.
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    Order 3 (1987), S. 359-367 
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    Keywords: 06A10 ; 68C25 ; Ordered set ; jump number ; matching ; dynamic programming ; bipartite permutation graphs
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    Notes: Abstract Let L=u 1 , u 2 , ..., u k be a linear extension of a poset P. Each pair (u i , u i+1 ) of unrelated elements in P is called a jump of L. The jump number problem is to find L with the minimum number of jumps. The problem is known to be NP-hard even on bipartite posets. Here we present a linear time algorithm for it in 2-dimensional bipartite posets. We also discuss briefly some weighted cases.
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    Order 4 (1987), S. 31-35 
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    Keywords: 06A10 ; Partial order ; linear extension ; monotone function ; acyclic function
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    Notes: Abstract Given a poset (A, r) and an acyclic r-monotone function f: A→A, we prove that r can be extended to a linear order R with xRy⇛f(x)Rf(y) for all x, y∈A.
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    Order 4 (1987), S. 101-106 
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    Keywords: 06A10 ; Ordered set ; width ; fixed point ; chain-completeness ; four-crown tower ; belfry
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    Notes: Abstract We consider the fixed point property (FPP) in an ordered set of width two (every antichain contains at most two elements). The necessary condition of the FPP and a number of equivalent conditions to the FPP in such sets is established. The product theorem is proved, as well.
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    Order 4 (1987), S. 285-291 
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    Keywords: 06A10 ; Partial order ; deficiency ; incomparable pairs
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    Notes: Abstract The deficiency of a partial order is the number of incomparable pairs. Another measure, the spread of a partial order is defined and its relation to the deficiency is established. In certain cases which arise naturally in the analysis of various sorting and selection algorithms where the partial order is only implicitly defined, the spread of the partial order is easier to estimate directly and provides a convenient way to estimate the deficiency.
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    Order 5 (1988), S. 17-20 
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    Keywords: 06A10 ; 06A23 ; Lattice ; order dimension ; least size
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    Notes: Abstract We investigate the behavior of f(d), the least size of a lattice of order dimension d. In particular we show that the lattice of a projective plane of order n has dimension at least n/ln(n), so that f(d)=O(d) 2 log2 d. We conjecture f(d)=θ(d 2 ), and prove something close to this for height-3 lattices, but in general we do not even know whether f(d)/d→∞.
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    Order 5 (1988), S. 33-43 
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    Keywords: 06A10 ; 68C05 ; Diagram ; tree ; orientation ; width ; algorithm
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    Notes: Abstract There are 2 n-1 ways in which a tree on n vertices can be oriented. Each of these can be regarded as the (Hasse) diagram of a partially ordered set. The maximal and minimal widths of these posets are determined. The maximal width depends on the bipartition of the tree as a bipartite graph and it can be determined in time O(n). The minimal width is one of [λ/2] or [λ/2]+1, where λ is the number of leaves of the tree. An algorithm of execution time O(n + λ2 log λ) to construct the minimal width orientation is given.
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    Order 5 (1988), S. 143-147 
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    Keywords: 06A10 ; Partial order ; dimension ; N-free
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    Notes: Abstract The dimension of a partial order can be multiplied by an arbitrarily large factor when edges are subdivided.
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    Order 5 (1988), S. 239-244 
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    Keywords: 06A10 ; Poset ; structural decomposition ; characterization
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    Notes: Abstract In this paper we show that the number of pairwise nonisomorphic two-dimensional posets with n elements is asymptotically equivalent to 1/2n!. This estimate is based on a characterization, in terms of structural decomposition, of two-dimensional posets having a unique representation as the intersection of two linear extensions.
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    Order 5 (1988), S. 289-304 
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    Keywords: 06A10 ; 54D30 ; Maximal chain ; cutset ; Menger's theorem
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    Notes: Abstract We prove the following results which are related to Menger's theorem for (infinite) ordered sets. (i) If the space of maximal chains of an ordered set is compact, then the maximum number of pairwise disjoint maximal chains is finite and is equal to the minimum size of a cutset, (i.e. a set which meets all maximal chains). (ii) If the maximal chains pairwise intersect, then the intersection of finitely many is never empty. One corollary of (ii) is that, if the maximal chains pairwise intersect and if one of the maximal chains is complete, then there is an element common to all maximal chains.
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    Order 5 (1989), S. 363-368 
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    Keywords: 06A10 ; 60F20 ; Partially ordered set ; random structure ; 0–1 law
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    Notes: Abstract We show that the 0–1 law fails in random orders of fixed dimension k, k≥3. In particular, we give an example of a first-order sentence ϕ, in the language of partial orders, which cannot have limiting probability 0 or 1 among random orders of dimension 3.
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    Order 5 (1989), S. 407-423 
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    Keywords: 06A10 ; 06C99 ; 06D99 ; Modular ordered set ; distributive ordered set ; strong subset ; LU subset
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    Notes: Abstract As modular and distributive ordered sets generalize modular and distributive lattices, it is a natural question to ask whether there exist some ‘forbidden configurations’ for those ordered sets. We present such configurations in the form of strong subsets and LU subsets.
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    Order 6 (1989), S. 15-18 
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    Keywords: 06A10 ; Linear extension ; promotion ; comparability graph
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    Notes: Abstract The number e(P) of linear extensions of a finite poset P is expressed in terms of e(Q) for certain smaller posets Q. The proof is based on M. Schützengerger's concept of promotions of linear extensions.
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    Order 6 (1989), S. 209-218 
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    Keywords: 06A10 ; Ordered set ; pagenumber ; booknumber ; planarity ; linear extension ; linear layout
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    Notes: Abstract General bounds for the pagenumber of an ordered set are developed. One bound is derived by first showing that the maximum number of edges in the diagram of a planar ordered setP is 2v(P)-2-ht(P). A construction is given to show that the pagenumber of the product ofn chains is no more than 2n-2. Lastly, some open questions are discussed.
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    Order 6 (1989), S. 241-244 
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    Keywords: 06A10 ; Linear extensions ; comparability graph
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    Notes: Abstract In this note, we prove that the comparability graph of a posetP has less edges than that of a posetQ on the same set of elements, thenP has more linear extensions thanQ. This solves a problem posed by Kelly [1].
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    Order 6 (1989), S. 295-303 
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    Keywords: 06A10 ; 68C25 ; Depth-first linear extension ; greedy linear extension ; ordered set ; NP-complete
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    Notes: Abstract We show that the problems of deciding whether an ordered set has at leastk depth-first linear extensions and whether an ordered set has at leastk greedy linear extensions are NP-hard.
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    Order 1 (1985), S. 229-233 
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    Keywords: 06A10 ; Partially ordered sets ; imbedding ; embedding ; linear extension
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    Notes: Abstract An imbedding of a poset P in the integers is a one-to-one order presevring map from P into the integers. Such a map always exists when P is finite and, moreover, certain imbeddings of subsets of finite P can be extended to imbeddings of the whole of P. D. E. Daykin has asked when an imbedding in the integers of a finite subset of a countable poset can be extended to the whole poset. This paper answers Daykin's question and some related questions.
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    Order 3 (1986), S. 155-158 
    ISSN: 1572-9273
    Keywords: 06A10 ; Comparability graph ; ordered set
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    Topics: Mathematics
    Notes: Abstract We study some invariants of finite comparability graphs.
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    Order 5 (1988), S. 23-32 
    ISSN: 1572-9273
    Keywords: 06A10 ; 06B05 ; Meet distributive lattices ; convex geometries ; convex dimension
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    Topics: Mathematics
    Notes: Abstract We develop a representation theory for convex geometries and meet distributive lattices in the spirit of Birkhoff's theorem characterizing distributive lattices. The results imply that every convex geometry on a set X has a canonical representation as a poset labelled by elements of X. These results are related to recent work of Korte and Lovász on antimatroids. We also compute the convex dimension of a convex geometry.
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    Order 5 (1988), S. 75-83 
    ISSN: 1572-9273
    Keywords: 06A10 ; 54D30 ; Ordered set ; maximal chain ; cutset ; Menger's theorem
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    Topics: Mathematics
    Notes: Abstract It is shown that if a chain complete ordered set does not have k+1 pairwise disjoint maximal chains for some finite k, then the minimum size of a cutset is equal to the maximum size of a collection of pairwise disjoint maximal chains. This answers a question of Pouzet and Zaguia.
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  • 74
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    Order 4 (1987), S. 143-154 
    ISSN: 1572-9273
    Keywords: 06A10 ; 68C25 ; Jump number ; greedy linear extensions ; Dilworth posets ; satisfiability
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    Topics: Mathematics
    Notes: Abstract Following the pioneering work of Kierstead, we present here some complexity results about the construction of depth-first greedy linear extensions. We prove that the recognition of Dilworth partially ordered sets of height 2, as defined by Syslo, is NP-complete. This last result yields a new proof of the NP-completeness of the jump number problem, first proved by Pulleyblank.
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    Order 4 (1987), S. 195-206 
    ISSN: 1572-9273
    Keywords: 68C15 ; 06A10 ; Posets ; preemptive ; scheduling
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    Topics: Mathematics
    Notes: Abstract In scheduling jobs subject to precedence constraints that form a partial order, it is advantageous to interrupt (preempt) jobs, and return to complete them at a later time in order to minimize total completion time. It is clearly desirable to see that such preemptive scheduling by finitely many machines requires only intervals of work, and not a more general assignment of tasks over measurable sets, for optimal completion. It is a deeper fact that arbitrarily small intervals are required for a fixed number of machines m〉-3 for optimal preemptive scheduling. On the other hand, if the number of jobs is fixed, say n, then it is intuitively clear that it suffices to use only comparatively large intervals (but less clear ‘how large’ will suffice!). The authors address these and certain related questions.
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    Order 4 (1987), S. 221-231 
    ISSN: 1572-9273
    Keywords: 06A10 ; Order preserving maps ; fixed point property ; product
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    Topics: Mathematics
    Notes: Abstract This problem motivates the present work: If ordered sets X and Y both have the fixed point property for order preserving maps has their product as well? Here we present a related condition — the so-called strong fixed point property — which arises from naive attempts to solve the problem. We are concerned with determining the nature and extent of this property. Several questions are raised concerning its relation to the fixed point property and other conditions such as dismantlability and contractibility.
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    Order 5 (1988), S. 149-161 
    ISSN: 1572-9273
    Keywords: 05C45 ; 05C70 ; 06A10 ; Hamiltonian cycle ; Boolean lattice ; lexicographic matching
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    Topics: Mathematics
    Notes: Abstract For any positive integer k let B(k) denote the bipartite graph of k- and k+1-element subsets of a 2k+1-element set with adjacency given by containment. It has been conjectured that for all k, B(k) is Hamiltonian. Any Hamiltonian cycle would be the union of two (perfect) matchings. Here it is shown that for all k〉1 no Hamiltonian cycle in B(k) is the union of two lexicographic matchings.
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    Order 5 (1988), S. 225-234 
    ISSN: 1572-9273
    Keywords: 06A10 ; Interval order ; circle order ; geometry
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    Topics: Mathematics
    Notes: Abstract A finite poset is an interval order if its point can be mapped into real intervals so that x〈y in the poset precisely when x's interval lies wholly to the left of y's; the poset is a circle order if its points can be mapped into circular disks in the plane so that x〈y precisely when x's circular disk is properly included in y's. This note proves that every finite interval order is a circle order.
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    Order 3 (1986), S. 257-267 
    ISSN: 1572-9273
    Keywords: 06A10 ; Ordered set ; chain ; core ; cutset ; fixed point ; chain-completeness ; dismantlability ; ordered sum ; fixed point property
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    Topics: Mathematics
    Notes: Abstract The purpose of this paper is the analysis and application of the concepts of a core (a pair of chains) and cutset in the fixed point theory for posets. The main results are: (1) (Theorem 3) If P is chain-complete and (*), it contains a cutset S such that every nonempty subset of S has a join or a meet in P, then P has the fixed point property (FPP), (2) (Theorem 5) If P or Q is chain-complete, Q satisfies (*) and both P and Q have the FPP, then P x Q has the FPP. (3) (Theorem 6) Let P or Q be chain-complete and there exist p∈P and a finite sequence f 1, f 2, ..., f n of order-preserving mappings of P into P such that $$\left( {\forall x\varepsilon P} \right)x \leqslant f_1 \left( x \right) \geqslant f_2 \left( x \right) \leqslant \cdots \geqslant f_n \left( x \right) \leqslant p$$ If P and Q have the FPP then P x Q has the FPP. (4) (Theorem 7) If T is an ordered set with the FPP and {P t :t∈T} is a disjoint family of ordered sets with the FPP then its ordered sum ∪{P t :t∈T} has the FPP.
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    Order 6 (1989), S. 227-233 
    ISSN: 1572-9273
    Keywords: 05A05 ; 05C45 ; 06A10 ; Combinatorial generation ; alternating permutation ; transposition
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    Topics: Mathematics
    Notes: Abstract A permutationπ 1 π 2...π n is alternating ifπ 1〈π 2〉π 3〈π 4.... Alternating permutations are counted by the Euler numbers. Here we show that alternating permutations can be listed so that successive permutations differ by a transposition, ifn is odd. Extensions and open problems are mentioned.
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    Order 6 (1989), S. 277-293 
    ISSN: 1572-9273
    Keywords: 06A10 ; Order dimension ; Ferrers dimension ; Cartesian product
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    Topics: Mathematics
    Notes: Abstract It is known that for incidence structures $$\mathbb{K}$$ and $$\mathbb{L}$$ , max $$\{ f{\text{ dim }}\mathbb{K}{\text{, }}f{\text{ dim }}\mathbb{L}{\text{\} }} \leqslant {\text{ }}f{\text{ dim }}\mathbb{K}{\text{ }}x{\text{ }}\mathbb{L} \leqslant f{\text{ dim }}\mathbb{K}{\text{ + }}f{\text{ dim }}\mathbb{L}$$ , wheref dim stands for Ferrers relation. We shall show that under additional assumptions on $$\mathbb{K}$$ and $$\mathbb{L}$$ , both bounds can be improved. Especially it will be shown that the square of a three-dimensional ordered set is at least four-dimensional.
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    Environmental management 10 (1986), S. 125-134 
    ISSN: 1432-1009
    Keywords: Wetlands ; Environmental characteristics ; Boundary definition ; Zonal properties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract Wetland environmental characteristics are examined to determine their spatial and temporal relationships. Two very different Oregon freshwater wetlands provided a range of wetland types. Results are evaluated to determine the possible use of environmental characteristics in defining wetlands and their boundaries. Representative physical, hydrological, and edaphic properties were periodically measured in microplots along upland/wetland transects. A multivariate approach is stressed in the data analysis; correlation, cluster analysis, and principal components analyses were used. The results indicate the environmental characteristics change in a quantifiable manner both spatially and temporally. The controlling mechanism is moisture, spatially in terms of the upland/wetland transect and temporally with respect to seasonal response. These changes do not correlate well with vegetation. Several hypotheses are offered as an explanation. Correlation within environmental characteristics is variable but definite patterns are discernible. These data suggest both single and combinations of environmental characteristics that could serve as “keys” in wetland identification and boundary determination. However, before extensive use is made of this information additional long-term monitoring of wetland environmental characteristics will be required.
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    Environmental management 10 (1986), S. 809-814 
    ISSN: 1432-1009
    Keywords: Wetlands ; Swamp ; Rights-of-way ; Vegetation ; Environmental impact
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    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract This study documents the effects of power utility right-of-way construction and maintenance on the vegetation of a wooded wetland in North Reading, Massachusetts, USA. Neither activity had a substantial, long-term negative impact. Except for differences in size and maturity, the vegetation recovered in two years from nearly total destruction caused by construction. Maintenance that included the periodic removal of high-growing species led to the formation of a plant association different from the one occurring naturally, but as diverse and species rich.
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    Environmental management 12 (1988), S. 181-192 
    ISSN: 1432-1009
    Keywords: Louisiana ; Mississippi Delta ; Sediment ; Accretion deficit ; Land loss ; Wetlands ; Management
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract Loss of Louisiana's coastal wetlands has reached catastrophic proportions. The loss rate is approximately 150 km2/yr (100 acres/day) and is increasing exponentially. Total wetland loss since the turn of the century has been almost 0.5 million ha (1.1 million acres) and represents an area larger than Rhode Island. The physical cause of the problem lies in man's attempts to control the Mississippi River's flooding, while enhancing navigation and extracting minerals. Levee systems and control structures confine sediments that once nourished the wetlands to the river channel. As a consequence, the ultimate sediment deposition is in deep Gulf waters off the Louisiana coast. The lack of sediment input to the interdistributary wetlands results in an accretion deficit. Natural and human-induced subsidence exceeds accretion so that the wetlands sink below sea level and convert to water. The solution is to provide a thin veneer of sediment (approximately 0.6 cm/yr; an average of 1450 g m−2 yr−1) over the coastal marshes and swamps and thus prevent the submergence of vegetation. The sediment source is the Mississippi River system. Calculations show that 9.2% of the river's annual suspended sediment load would be required to sustain the deltaic plain wetlands. It should be distributed during the six high-water months (December–June) through as disaggregated a network as possible. The problem is one of distribution: how can the maximum acres of marsh be nourished with the least cost? At present, the river is managed through federal policy for the benefit of navigation and flood control. A new policy structure, recognizing the new role for the river-sediment distribution, is recommended.
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    Environmental management 12 (1988), S. 639-653 
    ISSN: 1432-1009
    Keywords: Wetlands ; Water quality ; Cumulative impact
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    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract The total effect of cumulative impacts on the water quality functions of wetlands cannot be predicted from the sum of the effects each individual impact would have by itself. The wetland is not a simple filter; it embodies chemical, physical, and biotic processes that can detain, transform, release, or produce a wide variety of substances. Because wetland water quality functions result from the operation of many individual, distinct, and quite dissimilar mechanisms, it is necessary to consider the nature of each individual process. Sound knowledge of the various wetland processes is needed to make guided judgements about the probable effects of a given suite of impacts. Consideration of these processes suggests that many common wetland alterations probably do entail cumulative impact. In addition to traditional assessment methods, the wetland manager may need to obtain appropriate field measurements of water quality-related parameters at specific sites; such data can aid in predicting the effects of cumulative impact or assessing the results of past wetland management.
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    Environmental management 12 (1988), S. 695-701 
    ISSN: 1432-1009
    Keywords: Wetlands ; Wildlife ; Habitat ; Cumulative impacts ; Losses ; Perturbations ; Waterbirds
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract Wetlands are attractive to vertebrates because of their abundant nutrient resources and habitat diversity. Because they are conspicuous, vertebrates commonly are used as indicators of changes in wetlands produced by environmental impacts. Such impacts take place at the landscape level where extensive areas are lost; at the wetland complex level where some (usually small) units of a closely spaced group of wetlands are drained or modified; or at the level of the individual wetland through modification or fragmentation that impacts its habitat value. Vertebrates utilize habitats differently according to age, sex, geographic location, and season, and habitat evaluations based on isolated observations can be biased. Current wetland evaluation systems incorporate wildlife habitat as a major feature, and the habitat evaluation procedure focuses only on habitat. Several approaches for estimating bird habitat losses are derived from population curves based on natural and experimentally induced population fluctuations. Additional research needs and experimental approaches are identified for addressing cumulative impacts on wildlife habitat values.
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  • 87
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    Keywords: Cumulative impact assessment ; Wetlands ; Landscapes ; Functional grouping ; Temporal and spatial scale
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    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract The incongruity between the regional and national scales at which wetland losses are occurring, and the project-specific scale at which wetlands are regulated and studied, has become obvious. This article presents a synthesis of recent efforts by the US Environmental Protection Agency and the Ecosystems Research Center at Cornell University to bring wetland science and regulation into alignment with the reality of the cumulative effects of wetland loss and degradation on entire landscapes and regions. The synthesis is drawn from the other articles in this volume, the workshop that initiated them, and the scientific literature. It summarizes the status of our present scientific understanding, discusses means by which to actualize the existing potential for matching the scales of research and regulation with the scales at which effects are observed, and provides guidelines for building a stronger scientific base for landscape-level assessments of cumulative effects. It also provides the outlines for a synoptic and qualitative approach to cumulative effects assessment based on a reexamination of the generic assessment framework we proposed elsewhere in this volume. The primary conclusion to be drawn from the articles and the workshop is that a sound scientific basis for regulation will not come merely from acquiring more information on more variables. It will come from recognizing that a perceptual shift to larger temporal, spatial, and organizational scales is overdue. The shift in scale will dictate different—not necessarily more—variables to be measured in future wetland research and considered in wetland regulation.
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    Environmental management 12 (1988), S. 565-583 
    ISSN: 1432-1009
    Keywords: Cumulative impact assessment ; Wetlands ; Landscapes
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    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract This article outlines conceptual and methodological issues that must be confronted in developing a sound scientific basis for investigating cumulative effects on freshwater wetlands. We are particularly concerned with: (1) effects expressed at temporal and spatial scales beyond those of the individual disturbance, specific project, or single wetland, that is, effects occurring at the watershed or regional landscape level; and (2) the scientific (technical) component of the overall assessment process. Our aim is to lay the foundation for a research program to develop methods to quantify cumulative effects of wetland loss or degradation on the functioning of interacting systems of wetlands. Toward that goal we: (1) define the concept of cumulative effects in terms that permit scientific investigation of effects; (2) distinguish the scientific component of cumulative impact analysis from other aspects of the assessment process; (3) define critical scientific issues in assessing cumulative effects on wetlands; and (4) set up a hypothetical and generic structure for measuring cumulative effects on the functioning of wetlands as landscape systems. We provide a generic framework for evaluating cumulative effects on three basic wetland landscape functions: flood storage, water quality, and life support. Critical scientific issues include appropriate delineations of scales, identification of threshold responses, and the influence on different functions of wetland size, shape, and position in the landscape. The contribution of a particular wetland to landscape function within watersheds or regions will be determined by its intrinsic characteristics, e.g., size, morphometry, type, percent organic matter in the sediments, and hydrologic regime, and by extrinsic factors, i.e., the wetland's context in the landscape mosaic. Any cumulative effects evaluation must take into account the relationship between these intrinsic and extrinsic attributes and overall landscape function. We use the magnitude of exchanges among component wetlands in a watershed or larger landscape as the basis for defining the geographic boundaries of the assessment. The time scales of recovery for processes controlling particular wetland functions determine temporal boundaries. Landscape-level measures are proposed for each function.
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    Environmental management 13 (1989), S. 477-483 
    ISSN: 1432-1009
    Keywords: Wetlands ; Utility rights-of-way ; Vegetation-Environmental impact assessment ; Eastern Massachusetts
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract Utility rights-of-way corridors through wetland areas generate long-term impacts from construction activities to these valuable ecosystems. Changes to and recovery of the vegetation communities of a cattail marsh, wooded swamp, and shrub/bog wetland were documented through measurements made each growing season for two years prior, five years following, and again on the tenth year after construction of a 345-kV transmission line. While both the cattail marsh and wooded swamp recovered within a few years, measures of plant community composition in the shrub/bog wetland were still lower, compared to controls, after ten years. Long-term investigations such as the one reported here help decrease uncertainty and provide valuable information for future decision making regarding construction of power utility lines through valuable and dwindling wetland resources.
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  • 90
    ISSN: 1432-1009
    Keywords: Marsh loss ; Louisiana ; Wetlands ; Coastal zone management ; Saltwater intrusion ; Canal impacts
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract A computerized geographic information system with site-specific change-detection capabilities was developed to document amounts, rates, locations, and sequences of loss of coastal marsh to open water in Barataria Basin, Louisiana, USA. Land-water interpretations based on 1945, 1956, 1969, and 1980 aerial photographs were used as input, and a modified version of the Earth Resources Laboratory Applications Software developed by the National Aeronautics and Space Administration was used as a spatial data base management system. Analysis of these data sets indicates that rates of marsh loss have increased from 0.36% per year in the 1945–56 period, to 1.03% per year in 1956–69, and to 1.96% per year in 1969–80. The patterns of marsh loss indicate that the combination of processes causing degradation of the marsh surface does not affect all areas uniformly. Marsh loss rates have been highest where freshwater marshes have been subject to saltwater intrusion. The increase in the wetland loss rates corresponds to accelerated rates of subsidence and canal dredging and to a cumulative increase in the area of canals and spoil deposits.
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  • 91
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    Keywords: Landscape ecology ; Wetlands ; Ecological succession ; Spatiotemporal scales ; Stability, recovery
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract The wetland ecosystems occurring within alluvial floodplains change rapidly. Within the ecological successions, the life span of pioneer and transient stages may be measured in several years or decades depending on the respective influences of allogenic (water dynamics, erosion, and deposition) and autogenic developmental processes (population dynamics, eutrophication, and terrestrialization). This article emphasizes the mechanisms that are responsible for the ecosystem changes and their importance to environmental management. Two case studies exemplify reversible and irreversible successional processes in reference to different spatial and temporal scales. On the scale of the former channels, the standing-water ecosystems with low homeostasis may recover their previous status after human action on the allogenic processes. On the scale of a whole reach of the floodplain, erosion and deposition appear as reversible processes that regenerate the ecological successions. The concepts of stability and reversibility are discussed in relation to different spatiotemporal referential frameworks and different levels of integration. The reversible process concept is also considered with reference to the energy inputs into the involved subsystems. To estimate the probability of ecosystem regeneration or the cost of restoration, a concept of “degrees of reversibility” is proposed.
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    Environmental management 11 (1987), S. 823-836 
    ISSN: 1432-1009
    Keywords: Backfilling ; Mitigation ; Wetlands ; Louisiana ; Dredging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract Returning canal spoil banks into canals, or backfilling, is used in Louisiana marshes to mitigate damage caused by dredging for oil and gas extraction. We evaluated 33 canals backfilled through July 1984 to assess the success of habitat restoration. We determined restoration success by examining canal depth, vegetation recolonization, and regraded spoil bank soils after backfilling. Restoration success depended on: marsh type, canal location, canal age, marsh soil characteristics, the presence or absence of a plug at the canal mouth, whether mitigation was on- or off-site, and dredge operator performance. Backfilling reduced median canal depth from 2.4 to 1.1 m, restored marsh vegetation on the backfilled spoil bank, but did not restore emergent marsh vegetation in the canal because of the lack of sufficient spoil material to fill the canal and time. Median percentage of cover of marsh vegetation on the canal spoil banks was 51.6%. Median percentage of cover in the canal was 0.7%. The organic matter and water content of spoil bank soils were restored to values intermediate between spoil bank levels and predredging marsh conditions. The average percentage of cover of marsh vegetation on backfilled spoil banks was highest in intermediate marshes (68.6%) and lowest in fresh (34.7%) and salt marshes (33.9%). Average canal depth was greatest in intermediate marshes (1.50 m) and least in fresh marshes (0.85 m). Canals backfilled in the Chenier Plain of western Louisiana were shallower (average depth = 0.61 m) than in the eastern Deltaic Plain (mean depth range = 1.08 to 1.30 m), probably because of differences in sediment type, lower subsidence rate, and lower tidal exchange in the Chenier Plain. Canals backfilled in marshes with more organic soils were deeper, probably as a result of greater loss of spoil volume caused by oxidation of soil organic matter. Canals ten or more years old at the time of backfilling had shallower depths after backfilling. Depths varied widely among canals backfilled within ten years of dredging. Canal size showed no relationship to canal depth or amount of vegetation reestablished. Plugged canals contained more marsh reestablished in the canal and much greater chance of colonization by submerged aquatic vegetation compared with unplugged canals. Dredge operator skill was important in leveling spoil banks to allow vegetation reestablishment. Wide variation in dredge performance led to differing success of vegetation restoration. Complete reestablishment of the vegetation was not a necessary condition for successful restoration. In addition to providing vegetation reestablishment, backfilling canals resulted in shallow water areas with higher habitat value for benthos, fish, and waterfowl than unfilled canals. Spoil bank removal also may help restore water flow patterns over the marsh surface. Increased backfilling for wetland mitigation and restoration is recommended.
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    Environmental management 12 (1988), S. 591-602 
    ISSN: 1432-1009
    Keywords: Bottomland hardwood forests ; Cumulative impacts ; Goal-setting ; Regulation ; Wetlands
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract This article is an extension and application of Preston and Bedford (1988), especially as relevant to bottomland hardwood (BLH) forests of the southeastern United States. The most important cumulative effects in BLH forests result from incremental forest loss (nibbling) and from synergisms resulting from this nibbling. Present regulatory procedures are ineffective in preventing incremental forest loss because of the focus on permit site evaluation, rather than on large landscapes. Three examples are given to illustrate the need for a landscape focus. This perspective requires preplanning or goal-setting to establish the desired conditions to be maintained in the regulated landscape unit. Spatial and temporal scales are of particular concern for landscape impact assessment. Natural drainage basins of about 106 ha, as identified in U.S. Geological Survey hydrologic units, appear to appropriate spatial units: they have fairly natural boundaries, are of sufficient size to support populations of large, wide-ranging mammals, and are compatible with existing maps and databases. Time scales should be sufficiently long to include recovery of wetland ecosystems from human perturbations. In practice, available data sets limit analysis to no longer than 50 yr. Eight indicators of landscape integrity are identified, based on generally available long-term data sets. Linking technical information concerning cumulativeeffects on landscapes to the evaluation of cumulativeimpacts in regulatory programs (i.e., goal-setting) is a serious issue that can benefit from precedents found in the field of epidemiology, and in the establishment of clean air and clean water standards. We suggest that reference data sets must be developed, relating BLH function to structure (forest area). These can be used to set goals for individual watersheds, based on their present conditions and the magnitude and type of perceived development pressures. Thus the crucial steps in establishing a successful program appear to be (1) establish study unit boundaries, (2) assess the condition of study unit landscape integrity, (3) set goals, and (4) consider the impacts of permit proposals with both goals and the existing condition of the study unit landscape in mind.
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    Environmental management 13 (1989), S. 207-213 
    ISSN: 1432-1009
    Keywords: Wetlands ; Assessment technique ; Environmental impact ; Habitat evaluation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract This article presents a wetland habitat assessment technique (HAT) using birds as indicators of habitat quality. The technique is quick, simple, inexpensive, and lends itself to screening large numbers of wetlands. HAT can provide input to more extensive evaluation techniques. Measures of species diversity and rarity are used to assess the quality of the wetland. By applying the notion of ecologically optimum size, the technique addresses the issue of economic efficiency. Results of field testing HAT on 11 tidally influenced wetlands are presented to illustrate HAT's utility. Application of HAT in a variety of situations is discussed.
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    Environmental management 10 (1986), S. 107-112 
    ISSN: 1432-1009
    Keywords: Boundaries ; Conservation ; Hydrophytes ; Marsh ; Shoreline ; Wetlands ; Zonation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract There is an increasing need for the accurate delineation of wetlands for planning and conservation purposes. We propose a method based on vegetation zonation which requires three steps. The first step is to examine transects crossing the transition zone from marsh to upland. In each transect the uppermost occurrence of each plant species is located relative to a fixed survey point. The second step is to determine which of these species are hydrophytes (wetland plants). This is assessed using the presence or absence of morphological and physiological adaptations for growing in wet environments. Alternatively, a literature search using botanical manuals may suffice. The third step determines the upper limit of the wetland by finding the upper limit of the uppermost hydrophyte in each transect, and taking the mean value of these over all transects. This mean defines the boundary of the wetland. The method is illustrated using two marshes along the north shore of the St. Lawrence River in Ontario.
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  • 96
    ISSN: 1432-1009
    Keywords: Reservoirs ; Pollution ; Watershed ; Aquatic communities ; Riparian vegetation ; Wetlands ; Productivity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract A study of the impact of two flood control reservoirs and pollution influx was conducted on two streams within the Sandy Creek Watershed, Mercer County, Pennsylvania, USA. Fecal coliforms were significantly reduced in the outflows without affecting water chemistry, thereby improving the overall water quality. The size and composition of the aquatic communities as well as stream metabolism varied seasonably among the different sampling stations. Pollution influx primarily from communities and agricultural drainage had a greater impact on the stream ecosystem than did impounding of the streams. Natural wetlands and riparian vegetation were important factors in reducing the pollution load in these streams. The reestablishment and maintenance of riparian vegetation should therefore be an integral part of the land-use plan for watersheds in order to improve water quality and wildlife habitats. In the future, the maintenance of riparian vegetation should be given prime consideration in the development of watershed projects.
    Type of Medium: Electronic Resource
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  • 97
    Electronic Resource
    Electronic Resource
    Springer
    Environmental management 10 (1986), S. 145-156 
    ISSN: 1432-1009
    Keywords: Wetland management ; Wetlands ; Dredge and fill permit ; State wetland laws ; Wetland protection ; US Corps of Engineers
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract As inland wetlands face increasing pressure for development, both the federal government and individual states have begun reevaluating their respective wetland regulatory schemes. This article focuses first on the effectiveness of the past, present, and proposed federal regulations, most notably the Section 404, Dredge and Fill Permit Program, in dealing with shrinking wetland resources. The article then addresses the status of state involvement in this largely federal area, as well as state preparedness to assume primacy should federal priorities change. Finally, the subject of comprehensive legislation for wetland protection is investigated, and the article concludes with some procedural suggestions for developing a model law.
    Type of Medium: Electronic Resource
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  • 98
    Electronic Resource
    Electronic Resource
    Springer
    Environmental management 11 (1987), S. 29-34 
    ISSN: 1432-1009
    Keywords: Wetlands ; Coal mining ; Surface mining ; Pennsylvania
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract The impact of surface mining for coal on the nature and extent of freshwater wetlands was assessed on 73,200 ha in western Pennsylvania. The influence of mining on wetlands was not uniform across physiographic regions, varying with regional differences in hydrology and soils. Overall, mined lands supported 18% more palustrine wetlands than unmined lands, primarily because of a 270% gain in permanent, open-water wetlands on mined lands in the glaciated region. Open-water wetlands declined on mined lands in unglaciated regions owing to unfavorable hydrologic conditions. The number and size of emergent wetlands declined as a result of mining. Mined lands supported 81% fewer riverine wetlands than unmined lands. This was caused primarily by avoidance of lands containing streams, and secondarily by a 10% reduction in replacement of riverine wetlands during reclamation. Land managers need to develop land use policies that maximize the ecological and social benefits that can be derived from developing diverse wetland communities on mined lands.
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  • 99
    Electronic Resource
    Electronic Resource
    Springer
    Environmental management 11 (1987), S. 771-773 
    ISSN: 1432-1009
    Keywords: Soil conservation ; Wetlands ; Pond bottoms ; Phalaris arundinacea L ; Reed Canary Grass ; Connecticut
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract After the June 1982 floods in Essex, Connecticut, USA, reseeding for stabilization of exposed pond bottoms and subsequent rebuilding of a dam on the Mill Pond, Essex, CT resulted in rooted, floating aquatic mats ofPhalaris arundinacea L. This required that the site be weed harvested to restore open water. It is suggested that the species not be used to temporarily stabilize pond bottom soils because of its great and unexpected adaptability to aquatic situations.
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  • 100
    Electronic Resource
    Electronic Resource
    Springer
    Environmental management 12 (1988), S. 37-53 
    ISSN: 1432-1009
    Keywords: Wetlands ; Marsh management ; Louisiana ; Impoundment ; Water control structures
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract Louisiana's coastal wetlands represent about 41% of the nation's total and are extensively managed for fish, fur, and waterfowl. Marsh management plans (MMPs) are currently used to avoid potential user conflicts and are believed to be a best management practice for specific management goals. In this article, we define MMPs and examine their variety, history, impacts, and future. A MMP is an organized written plan submitted to state and federal permitting agencies for approval and whose purpose is to regulate wetland habitat quantity and quality (control land loss and enhance productivity). MMPs are usually implemented by making structural modifications in the marsh, primarily by using a variety of water control structures in levees to impound or semi-impound managed areas. It appears that MMPs using impoundments are only marginally successful in achieving and often contradict management goals. Although 20% of coastal Louisiana may be in MMPs by the year 2000, conflict resolution of public and private goals is compromised by a surfeit of opinion and dearth of data and experience. Based on interpretation of these results, we believe the next phase of management should include scientific studies of actual impacts, utilization of post-construction monitoring data, inventory of existing MMPs, development of new techniques, and determination of cumulative impacts.
    Type of Medium: Electronic Resource
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