منابع مشابه
Chordal and Sequentially Cohen-Macaulay Clutters
We extend the definition of chordal from graphs to clutters. The resulting family generalizes both chordal graphs and matroids, and obeys many of the same algebraic and geometric properties. Specifically, the independence complex of a chordal clutter is shellable, hence sequentially Cohen-Macaulay; and the circuit ideal of a certain complement to such a clutter has a linear resolution. Minimal ...
متن کاملCohen-Macaulay clutters with combinatorial optimization properties and parallelizations of normal edge ideals
Let C be a uniform clutter and let I = I(C) be its edge ideal. We prove that if C satisfies the packing property (resp. max-flow min-cut property), then there is a uniform Cohen-Macaulay clutter C1 satisfying the packing property (resp. max-flow min-cut property) such that C is a minor of C1. For arbitrary edge ideals of clutters we prove that the normality property is closed under parallelizat...
متن کاملCohen-macaulay, Shellable and Unmixed Clutters with a Perfect Matching of König Type
Let C be a clutter with a perfect matching e1, . . . , eg of König type and let ∆C be the Stanley-Reisner complex of the edge ideal of C. If all c-minors of C have a free vertex and C is unmixed, we show that ∆C is pure shellable. We are able to describe in combinatorial terms when ∆C is pure. If C has no cycles of length 3 or 4, then it is shown that ∆C is pure if and only if ∆C is pure shella...
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 Commutative Algebra
سال: 2009
ISSN: 1939-2346
DOI: 10.1216/jca-2009-1-3-463