Multigraded minimal free resolutions of simplicial subclutters

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:178

Article

Bigdeli, Mina¹  Pour, Ali Akbar Yazdan² 

[1] Inst Res Fundamental Sci IPM, Sch Math, POB 19395-5746, Tehran, Iran

[2] Inst Adv Studies Basic Sci IASBS, Dept Math, POB 45195-1159, Zanjan, Iran

关键词: Betti number;    Linear resolution;    Regularity;    Chordal clutter;    Simplicial subclutter;   

DOI  :  10.1016/j.jcta.2020.105339

来源: Elsevier

【 摘 要 】

This paper concerns the study of a class of clutters called simplicial subclutters. Given a clutter C and its simplicial subclutter D, we compare some algebraic properties and invariants of the ideals I, J associated to these two clutters, respectively. We give a formula for computing the (multi)graded Betti numbers of J in terms of those of I and some combinatorial data about D. As a result, we see that if C admits a simplicial subclutter, then there exists a monomial u is not an element of I such that the (multi)graded Betti numbers of I (u) can be computed through those of I. It is proved that the Betti sequence of any graded ideal with linear resolution is the Betti sequence of an ideal associated to a simplicial subclutter of the complete clutter. These ideals turn out to have linear quotients. However, they do not form all the equigenerated square-free monomial ideals with linear quotients. If C admits empty set as a simplicial subclutter, then I has linear resolution over all fields. Examples show that the converse is not true. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free