Cohen-Macaulay Properties of Square-Free Monomial Ideals

Details Cohen-Macaulay Properties of Square-Free Monomial Ideals Cohen-Macaulay Properties of Square-Free Monomial Ideals

2003-07-31

arxiv.org/abs/math/0307403v2

J. Combin. Theory Ser. A 109 (2005), no. 2, 299--329

Mathematics

Commutative Algebra

28 pages, 17 figures

Scientific paper

In this paper we study simplicial complexes as higher dimensional graphs in order to produce algebraic statements about their facet ideals. We introduce a large class of square-free monomial ideals with Cohen-Macaulay quotients, and a criterion for the Cohen-Macaulayness of facet ideals of simplicial trees. Along the way, we generalize several concepts from graph theory to simplicial complexes.

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