Cohen-Macaulay Connectivity and Geometric Lattices
نویسندگان
چکیده
منابع مشابه
On the Cohen-Macaulay connectivity of supersolvable lattices and the homotopy type of posets
It is a well known fact that a supersolvable lattice is ELoshellable. Hence a supersolvable lattice (resp., its Stanley-Reisner ring) is Cohen-Macaulay. We prove that if L is a supersolvable lattice such that all intervals have non-vanishing Mt~bius number, then for an arbitrary element x e L the poser L {x} is also Cohen-Macaulay. Posets with this property are called 2-Cohen-Macaulay posets. I...
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Chari proved that if ∆ is a (d − 1)-dimensional simplicial complex with a convex ear decomposition, then h0 ≤ · · · ≤ hbd/2c [7]. Nyman and Swartz raised the problem of whether or not the corresponding g-vector is an M -vector [18]. This is proved to be true by showing that the set of pairs (ω,Θ), where Θ is a l.s.o.p. for k[∆], the face ring of ∆, and ω is a g-element for k[∆]/Θ, is nonempty w...
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Let Φ be a finite root system of rank n and let m be a positive integer. It is proved that the generalized cluster complex ∆m(Φ), introduced by S. Fomin and N. Reading, is (m + 1)-Cohen-Macaulay, in the sense of Baclawski. This statement was conjectured by V. Reiner. More precisely, it is proved that the simplicial complex obtained from ∆m(Φ) by removing any subset of its vertex set of cardinal...
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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: European Journal of Combinatorics
سال: 1982
ISSN: 0195-6698
DOI: 10.1016/s0195-6698(82)80014-0