Further applications of clutter domination parameters to projective dimension

JOURNAL OF ALGEBRA

卷:432

Article

关键词: Projective dimension;    Squarefree monomial ideal;    Clutter;    Hypergraph;    Domination parameter;    Stanley-Reisner complex;   

DOI  :  10.1016/j.jalgebra.2015.03.001

来源: Elsevier

【 摘 要 】

We study the relationship between the projective dimension of a squarefree monomial ideal and the domination parameters of the associated graph or clutter. In particular, we show that the projective dimensions of graphs with perfect dominating sets can be calculated combinatorially. We also generalize the well-known graph domination parameter tau to clutters, obtaining bounds on the projective dimension analogous to those for graphs. Through Hochster's Formula, our bounds on projective dimension also give rise to bounds on the homologies of the associated Stanley Reisner complexes. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

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