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...
متن کاملCohen-Macaulay Partially Ordered Sets with Pure Resolutions
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...
متن کاملThe absolute order on the symmetric group, constructible partially ordered sets and Cohen-Macaulay complexes
The absolute order is a natural partial order on a Coxeter group W . It can be viewed as an analogue of the weak order on W in which the role of the generating set of simple reflections in W is played by the set of all reflections in W . By use of a notion of constructibility for partially ordered sets, it is proved that the absolute order on the symmetric group is homotopy Cohen–Macaulay. This...
متن کاملBi-Cohen-Macaulay graphs
In this paper we consider bi-Cohen-Macaulay graphs, and give a complete classification of such graphs in the case they are bipartite or chordal. General biCohen-Macaulay graphs are classified up to separation. The inseparable bi-CohenMacaulay graphs are determined. We establish a bijection between the set of all trees and the set of inseparable bi-Cohen-Macaulay graphs.
متن کاملCohen-macaulay Cell Complexes
We show that a finite regular cell complex with the intersection property is a Cohen-Macaulay space iff the top enriched cohomology module is the only nonvanishing one. We prove a comprehensive generalization of Balinski’s theorem on convex polytopes. Also we show that for any Cohen-Macaulay cell complex as above, although there is now generalization of the Stanley-Reisner ring of simplicial co...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1980
ISSN: 0021-8693
DOI: 10.1016/0021-8693(80)90033-2