Bounds on the regularity and projective dimension of ideals associated to graphs

被引：103

作者：

Dao, Hailong ^{[1
]}

Huneke, Craig ^{[1
]}

Schweig, Jay ^{[1
]}

机构：

[1] Univ Kansas, Dept Math, Lawrence, KS 66045 USA

来源：

JOURNAL OF ALGEBRAIC COMBINATORICS | 2013年 / 38卷 / 01期

基金：

美国国家科学基金会;

关键词：

Projective dimension; Regularity; Edge ideals; Serre's condition; LOCAL COHOMOLOGY; RESOLUTIONS; COMPLEXES;

D O I：

10.1007/s10801-012-0391-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we give new upper bounds on the regularity of edge ideals whose resolutions are k-step linear; surprisingly, the bounds are logarithmic in the number of variables. We also give various bounds for the projective dimension of such ideals, generalizing other recent results. By Alexander duality, our results also apply to unmixed square-free monomial ideals of codimension two. We also discuss and connect these results to more classical topics in commutative algebra.

引用

页码：37 / 55

页数：19

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