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  • Articles  (102)
  • Other Sources
  • Mathematics and Statistics  (83)
  • 06A10  (19)
  • 2000-2004
  • 1985-1989  (102)
  • 1950-1954
  • 1989  (102)
  • Mathematics  (102)
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  • Articles  (102)
  • Other Sources
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  • 2000-2004
  • 1985-1989  (102)
  • 1950-1954
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  • Mathematics  (102)
  • 1
    Electronic Resource
    Electronic Resource
    The PT-order, minimal cutsets and menger property (1989)
    Springer
    Order 6 (1989), S. 59-68 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00341637
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  • 2
    Electronic Resource
    Electronic Resource
    Semiorders and the 1/3–2/3 conjecture (1989)
    Springer
    Order 5 (1989), S. 369-380 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00353656
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  • 3
    Electronic Resource
    Electronic Resource
    Minimum cutsets for an element of a boolean lattice (1989)
    Springer
    Order 6 (1989), S. 31-37 
    Details
    ISSN: 1572-9273
    Keywords: 05A05 ; 06A10 ; Cutset ; Boolean lattice
    Source: Springer Online Journal Archives 1860-2000
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00341634
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  • 4
    Electronic Resource
    Electronic Resource
    Planar acyclic oriented graphs (1989)
    Springer
    Order 5 (1989), S. 349-361 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00353654
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  • 5
    Electronic Resource
    Electronic Resource
    Upper bound multigraphs for posets (1989)
    Springer
    Order 6 (1989), S. 265-275 
    Details
    ISSN: 1572-9273
    Keywords: 05C75 ; O5C99 ; 06A10 ; Upper bound graph ; multigraph ; poset ; chordal graph ; interval graph
    Source: Springer Online Journal Archives 1860-2000
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00563527
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  • 6
    Electronic Resource
    Electronic Resource
    The fixed point property for small sets (1989)
    Springer
    Order 6 (1989), S. 1-14 
    Details
    ISSN: 1572-9273
    Keywords: 06A10 ; Fixed point ; irreducible element ; dismantlability ; cutset ; retraction ; crown
    Source: Springer Online Journal Archives 1860-2000
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00341631
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  • 7
    Electronic Resource
    Electronic Resource
    Circle orders and angle orders (1989)
    Springer
    Order 6 (1989), S. 39-47 
    Details
    ISSN: 1572-9273
    Keywords: 06A10 ; Inclusion orders ; circle orders ; angle orders
    Source: Springer Online Journal Archives 1860-2000
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00341635
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  • 8
    Electronic Resource
    Electronic Resource
    Algebraic properties of crowns and fences (1989)
    Springer
    Order 6 (1989), S. 91-99 
    Details
    ISSN: 1572-9273
    Keywords: 08A40 ; 06A10 ; Clones ; crowns ; tences ; generators
    Source: Springer Online Journal Archives 1860-2000
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00341639
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  • 9
    Electronic Resource
    Electronic Resource
    Sphere orders (1989)
    Springer
    Order 6 (1989), S. 235-240 
    Details
    ISSN: 1572-9273
    Keywords: 06A10 ; 52A37 ; Order ; sphere ; partially ordered set ; space-time
    Source: Springer Online Journal Archives 1860-2000
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00563524
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  • 10
    Electronic Resource
    Electronic Resource
    Preemptive scheduling of interval orders is polynomial (1989)
    Springer
    Order 5 (1989), S. 345-348 
    Details
    ISSN: 1572-9273
    Keywords: 06A10 ; 68C15 ; Preemptive scheduling ; interval order
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00353653
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