Shellable and Cohen-Macaulay partially ordered sets
نویسندگان
چکیده
منابع مشابه
Shellable and Cohen-macaulay Partially Ordered Sets
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...
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1.1. Let V = {x1, x2, . . . , xv} be a finite set, called the vertex set, and 1 a simplicial complex on V . Thus 1 is a collection of subsets of V such that (i) {xi } ∈ 1 for every 1 ≤ i ≤ v and (ii) σ ∈ 1, τ ⊂ σ ⇒ τ ∈ 1. Each element σ of 1 is called a face of 1. Set d = max{#(σ ); σ ∈ 1}. Here #(σ ) is the cardinality of σ as a finite set. Then the dimension of 1 is defined by dim1 = d − 1. A...
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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...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1980
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1980-0570784-2