Signable posets and partitionable simplicial complexes
نویسندگان
چکیده
منابع مشابه
Signable Posets and Partitionable Simplicial Complexes
The notion of a partitionable simplicial complex is extended to that of a signable partially ordered set. It is shown in a unified way that face lattices of shellable polytopal complexes, polyhedral cone fans, and oriented matroid polytopes, are all signable. Each of these classes, which are believed to be mutually incomparable, strictly contains the class of convex polytopes. A general suffici...
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The class of Strongly Signable partially ordered sets is introduced and studied. It is show that strong signability, reminiscent of Björner–Wachs’ recursive coatom orderability, provides a useful and broad sufficient condition for a poset to be dual CR and hence partitionable. The flag h-vectors of strongly signable posets are therefore non-negative. It is proved that recursively shellable pose...
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We study Stanley decompositions and show that Stanley’s conjecture on Stanley decompositions implies his conjecture on partitionable Cohen-Macaulay simplicial complexes. We also prove these conjectures for all Cohen-Macaulay monomial ideals of codimension 2 and all Gorenstein monomial ideals of codimension 3.
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We establish an upper bound on the cardinality of a minimal generating set for the fundamental group of a large family of connected, balanced simplicial complexes and, more generally, simplicial posets.
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For several important classes of manifolds acted on by the torus, the information about the action can be encoded combinatorially by a regular n-valent graph with vector labels on its edges, which we refer to as the torus graph. By analogy with the GKM-graphs, we introduce the notion of equivariant cohomology of a torus graph, and show that it is isomorphic to the face ring of the associated si...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 1996
ISSN: 0179-5376,1432-0444
DOI: 10.1007/bf02711519