Chordality of clutters with vertex decomposable dual and ascent of clutters

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:168

Article

Nikseresht, Ashkan^1,2 

[1] Shiraz Univ, Dept Math, Shiraz 71457113565, Iran

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

关键词: Chordal clutter;    Linear resolution;    Vertex decomposable simplicial complex;    Ascent of a clutter;    Squarefree monomial ideal;   

DOI  :  10.1016/j.jcta.2019.06.007

来源: Elsevier

【 摘 要 】

In this paper, we consider the generalization of chordal graphs to clutters proposed by Bigdeli, et al. (2017) in [2]. Assume that (C) over bar is a d-dimensional uniform clutter. It is known that if C is chordal, then I(C) has a linear resolution over all fields. The converse has recently been rejected, but the following question which poses a weaker version of the converse is still open: if I((C) over bar) has linear quotients, is (C) over bar necessarily chordal?. Here, by introducing the concept of the ascent of a clutter, we split this question into two simpler questions and present some clues in support of an affirmative answer. In particular, we show that if I((C) over bar) is the Stanley-Reisner ideal of a simplicial complex with a vertex decomposable Alexander dual, then C is chordal. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free