ALBERT

All Library Books, journals and Electronic Records Telegrafenberg

X
feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
Filter
  • Books
  • Articles  (16)
  • Data
  • 06A10  (16)
  • 1995-1999
  • 1985-1989  (16)
  • 1950-1954
  • 1988  (16)
  • Mathematics  (16)
Collection
  • Books
  • Articles  (16)
  • Data
Source
Keywords
Publisher
Years
  • 1995-1999
  • 1985-1989  (16)
  • 1950-1954
Year
Topic
  • Mathematics  (16)
  • 1
    Electronic Resource
    Electronic Resource
    Explicit matchings in the middle levels of the Boolean lattice (1988)
    Springer
    Order 5 (1988), S. 163-171 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00337621
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    Dimension may exceed width (1988)
    Springer
    Order 5 (1988), S. 21-22 
    Details
    ISSN: 1572-9273
    Keywords: 06A10 ; Dimension ; width ; chain-covering number
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A partially ordered set with no infinite antichains may have arbitrarily large dimension.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00143894
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    On circle containment orders (1988)
    Springer
    Order 4 (1988), S. 315-318 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00714474
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 4
    Electronic Resource
    Electronic Resource
    χ-Embeddings of ordered sets (1988)
    Springer
    Order 5 (1988), S. 173-186 
    Details
    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’.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00337622
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 5
    Electronic Resource
    Electronic Resource
    A short proof that N 3 is not a circle containment order (1988)
    Springer
    Order 5 (1988), S. 235-237 
    Details
    ISSN: 1572-9273
    Keywords: 06A10 ; Circle containment order ; poset
    Source: Springer Online Journal Archives 1860-2000
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00354890
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 6
    Electronic Resource
    Electronic Resource
    Decompositions of partially ordered sets into chains and antichains of given size (1988)
    Springer
    Order 5 (1988), S. 245-255 
    Details
    ISSN: 1572-9273
    Keywords: 05C55 ; 05C70 ; 06A10 ; Decomposition ; Ramsey theory ; graph ; finite set system ; partially ordered set ; monotone sequence ; Δ-system ; chain ; antichain ; sub-k coloring
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00354892
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 7
    Electronic Resource
    Electronic Resource
    The Menger property for infinite ordered sets (1988)
    Springer
    Order 5 (1988), S. 305-315 
    Details
    ISSN: 1572-9273
    Keywords: 06A10 ; Ordered set ; maximal chain ; cutset ; Menger's theorem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00354897
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 8
    Electronic Resource
    Electronic Resource
    Dimension versus size (1988)
    Springer
    Order 5 (1988), S. 17-20 
    Details
    ISSN: 1572-9273
    Keywords: 06A10 ; 06A23 ; Lattice ; order dimension ; least size
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    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→∞.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00143893
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 9
    Electronic Resource
    Electronic Resource
    On the width of an orientation of a tree (1988)
    Springer
    Order 5 (1988), S. 33-43 
    Details
    ISSN: 1572-9273
    Keywords: 06A10 ; 68C05 ; Diagram ; tree ; orientation ; width ; algorithm
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00143896
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 10
    Electronic Resource
    Electronic Resource
    Edge subdivision and dimension (1988)
    Springer
    Order 5 (1988), S. 143-147 
    Details
    ISSN: 1572-9273
    Keywords: 06A10 ; Partial order ; dimension ; N-free
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The dimension of a partial order can be multiplied by an arbitrarily large factor when edges are subdivided.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00337619
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 11
    Electronic Resource
    Electronic Resource
    Asymptotic enumeration of two-dimensional posets (1988)
    Springer
    Order 5 (1988), S. 239-244 
    Details
    ISSN: 1572-9273
    Keywords: 06A10 ; Poset ; structural decomposition ; characterization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00354891
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 12
    Electronic Resource
    Electronic Resource
    Maximal chains and cutsets of an ordered set: A menger type approach (1988)
    Springer
    Order 5 (1988), S. 289-304 
    Details
    ISSN: 1572-9273
    Keywords: 06A10 ; 54D30 ; Maximal chain ; cutset ; Menger's theorem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00354896
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 13
    Electronic Resource
    Electronic Resource
    Combinatorial representation and convex dimension of convex geometries (1988)
    Springer
    Order 5 (1988), S. 23-32 
    Details
    ISSN: 1572-9273
    Keywords: 06A10 ; 06B05 ; Meet distributive lattices ; convex geometries ; convex dimension
    Source: Springer Online Journal Archives 1860-2000
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00143895
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 14
    Electronic Resource
    Electronic Resource
    A minimax theorem for chain complete ordered sets (1988)
    Springer
    Order 5 (1988), S. 75-83 
    Details
    ISSN: 1572-9273
    Keywords: 06A10 ; 54D30 ; Ordered set ; maximal chain ; cutset ; Menger's theorem
    Source: Springer Online Journal Archives 1860-2000
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00143899
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 15
    Electronic Resource
    Electronic Resource
    Lexicographic matchings cannot form Hamiltonian cycles (1988)
    Springer
    Order 5 (1988), S. 149-161 
    Details
    ISSN: 1572-9273
    Keywords: 05C45 ; 05C70 ; 06A10 ; Hamiltonian cycle ; Boolean lattice ; lexicographic matching
    Source: Springer Online Journal Archives 1860-2000
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00337620
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 16
    Electronic Resource
    Electronic Resource
    Interval orders and circle orders (1988)
    Springer
    Order 5 (1988), S. 225-234 
    Details
    ISSN: 1572-9273
    Keywords: 06A10 ; Interval order ; circle order ; geometry
    Source: Springer Online Journal Archives 1860-2000
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00354889
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...