نتایج جستجو برای: shellable complex

تعداد نتایج: 783934  

Journal: :J. Comb. Theory, Ser. A 2008
Adam Van Tuyl Rafael H. Villarreal

Associated to a simple undirected graph G is a simplicial complex ∆G whose faces correspond to the independent sets of G. We call a graph G shellable if ∆G is a shellable simplicial complex in the non-pure sense of Björner-Wachs. We are then interested in determining what families of graphs have the property that G is shellable. We show that all chordal graphs are shellable. Furthermore, we cla...

1980
ANDERS BJÖRNER

In this paper we study shellable posets (partially ordered sets), that is, finite posets such that the simplicial complex of chains is shellable. It is shown that all admissible lattices (including all finite semimodular and supersolvable lattices) and all bounded locally semimodular finite posets are shellable. A technique for labeling the edges of the Hasse diagram of certain lattices, due to...

Journal: :Electronic Journal of Combinatorics 2023

The augmented Bergman complex of a closure operator on finite set interpolates between the order proper flats and independence operator. In 2020, Braden, Huh, Matherne, Proudfoot, Wang showed that complexes matroids are always gallery-connected, recently Bullock, Kelley, Reiner, Ren, Shemy, Shen, Sun, Tao, Zhang strengthened "gallery-connected" to "shellable" by providing two classes shelling o...

Journal: :bulletin of the iranian mathematical society 2011
s. moradi d. kiani

we consider a class of hypergraphs called hypercycles and we show that a hypercycle $c_n^{d,alpha}$ is shellable or sequentially the cohen--macaulay if and only if $nin{3,5}$. also, we characterize cohen--macaulay hypercycles. these results are hypergraph versions of results proved for cycles in graphs.

Journal: :Homology, Homotopy and Applications 2022

We recently introduced a notion of tilings the geometric realization finite simplicial complex and related those to discrete Morse theory R. Forman, especially when they have property be shellable, shared by classical shellable complexes. now observe that every such tiling supports quiver which is acyclic precisely then shelling induces two spectral sequences converge (co)homology complex. Thei...

2001
JOHN SHARESHIAN

We show that the order complex of the subgroup lattice of a finite group G is nonpure shellable if and only if G is solvable. A by-product of the proof that nonsolvable groups do not have shellable subgroup lattices is the determination of the homotopy types of the order complexes of the subgroup lattices of many minimal simple groups.

Journal: :Electr. J. Comb. 1996
Art M. Duval

Björner and Wachs generalized the definition of shellability by dropping the assumption of purity; they also introduced the h-triangle, a doubly-indexed generalization of the h-vector which is combinatorially significant for nonpure shellable complexes. Stanley subsequently defined a nonpure simplicial complex to be sequentially Cohen-Macaulay if it satisfies algebraic conditions that generaliz...

2009
Sangwook Kim

We prove that if a simplicial complex ∆ is (nonpure) shellable, then the intersection lattice for the corresponding real coordinate subspace arrangement A∆ is homotopy equivalent to the link of the intersection of all facets of ∆. As a consequence, we show that the singularity link of A∆ is homotopy equivalent to a wedge of spheres. We also show that the complement of A∆ is homotopy equivalent ...

Journal: :Journal of Combinatorial Theory, Series A 2021

A recent conjecture that appeared in three papers by Bigdeli–Faridi, Dochtermann, and Nikseresht, is every simplicial complex whose clique has shellable Alexander dual, ridge-chordal. This strengthens the long-standing Simon's k-skeleton of simplex extendably shellable, for any k. We show stronger a negative answer, exhibiting an infinite family counterexamples.

2000
Karen L. Collins

The special properties of planar posets have been studied, particularly in the 1970's by I. Rival and others. More recently, the connection between posets, their corresponding polynomial rings and corresponding simplicial complexes has been studied by R. Stanley and others. This paper, using work of A. Bjorner, provides a connection between the two bodies of work, by characterizing when planar...

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