Cohen-Macaulay properties of square-free monomial ideals

摘要

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. (c) 2004 Elsevier Inc. All rights reserved.