Stability of Betti numbers under reduction processes: Towards chordality of clutters

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:145

Article

Bigdeli, Mina¹  Pour, Ali Akbar Yazdan¹  Zaare-Nahandi, Rashid¹ 

[1] IASBS, Dept Math, POB 45195-1159, Zanjan, Iran

关键词: Betti number;    Linear resolution;    Regularity;    Index;    Chordal clutter;   

DOI  :  10.1016/j.jcta.2016.06.001

来源: Elsevier

【 摘 要 】

For a given clutter C, let I := I ((C) over bar) be the circuit ideal in the polynomial ring S. In this paper, we show that the Betti numbers of I and I + (x(F)) are the same in their non-linear strands, for some suitable F epsilon C. Motivated by this result, we introduce a class of clutters that we call chordal This class is a natural extension of the class of chordal graphs and has the nice property that the circuit ideal associated to the complement of any member of this class has a linear resolution over any field. Finally we compare this class with all known families of clutters which generalize the notion of chordality, and show that our class contains several important previously defined classes of chordal clutters. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free