$k$-shellable simplicial complexes and graphs
نویسندگان
چکیده
منابع مشابه
New methods for constructing shellable simplicial complexes
A clutter $mathcal{C}$ with vertex set $[n]$ is an antichain of subsets of $[n]$, called circuits, covering all vertices. The clutter is $d$-uniform if all of its circuits have the same cardinality $d$. If $mathbb{K}$ is a field, then there is a one-to-one correspondence between clutters on $V$ and square-free monomial ideals in $mathbb{K}[x_1,ldots,x_n]$ as follows: To each clutter $mathcal{C}...
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Introduction Vertex decomposability of a simplicial complex is a combinatorial topological concept which is related to the algebraic properties of the Stanley-Reisner ring of the simplicial complex. This notion was first defined by Provan and Billera in 1980 for k-decomposable pure complexes which is known as vertex decomposable when . Later Bjorner and Wachs extended this concept to non-pure ...
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The construction of the Bier sphere Bier(K) for a simplicial complex K is due to Bier (1992). Björner, Paffenholz, Sjöstrand and Ziegler (2005) generalize this construction to obtain a Bier poset Bier(P, I) from any bounded poset P and any proper ideal I ⊆ P . They show shellability of Bier(P, I) for the case P = Bn, the boolean lattice, and thereby obtain ‘many shellable spheres’ in the sense ...
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Suppose a group G acts properly on a simplicial complex Γ . Let l be the number of G-invariant vertices, and p1,p2, . . . , pm be the sizes of the G-orbits having size greater than 1. Then Γ must be a subcomplex of Λ = Δl−1 ∗ ∂Δp1−1 ∗ · · · ∗ ∂Δpm−1. A result of Novik gives necessary conditions on the face numbers of Cohen–Macaulay subcomplexes of Λ. We show that these conditions are also suffi...
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We can construct the neighborhood complex N(G), with vertices v1, ..., vn, from the graph G, in such a way that, for each vertex v of G, there is a simplex containing the vertex v along with its neighbouring vertices, corresponding to the directed edges v → w. To construct this, we can take each vertex in v1, ..., vn one by one, and construct the simplex along with it’s neighbors, each time. Th...
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ژورنال
عنوان ژورنال: MATHEMATICA SCANDINAVICA
سال: 2018
ISSN: 1903-1807,0025-5521
DOI: 10.7146/math.scand.a-102975