Chorded complexes and a necessary condition for a monomial ideal to have a linear resolution

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:120

Article

Connon, E.¹  Faridi, S.¹ 

[1] Dalhousie Univ, Dept Math & Stat, Halifax, NS B3H 3J5, Canada

关键词: Linear resolution;    Monomial ideal;    Chordal graph;    Simplicial complex;    Simplicial homology;    Stanley-Reisner complex;    Facet complex;    Chordal hypergraph;   

DOI  :  10.1016/j.jcta.2013.05.009

来源: Elsevier

【 摘 要 】

In this paper we extend one direction of Frtiberg's theorem on a combinatorial classification of quadratic monomial ideals with linear resolutions. We do this by generalizing the notion of a chordal graph to higher dimensions with the introduction of d-chorded and orientably-d-cycle-complete simplicial complexes. We show that a certain class of simplicial complexes, the d-dimensional trees, correspond to ideals having linear resolutions over fields of characteristic 2 and we also give a necessary combinatorial condition for a monomial ideal to be componentwise linear over all fields. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free