Article ID Journal Published Year Pages File Type
9515382 Journal of Combinatorial Theory, Series A 2005 31 Pages PDF
Abstract
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.
Keywords
Related Topics
Physical Sciences and Engineering Mathematics Discrete Mathematics and Combinatorics
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