Chordality of clutters with vertex decomposable dual and ascent of clutters
Chordality of clutters with vertex decomposable dual and ascent of clutters
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具有顶点可分解对偶的杂波的弦性和杂波的上升
DOI：
10.1016/j.jcta.2019.06.007
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
A. Nikseresht
中科院分区：
文献类型：
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作者：
A. Nikseresht
在本文中，我们考虑了Bigdeli等人(2017)在[2]中提出的弦图到杂波的推广。假设C是d维均匀杂波。众所周知，如果C是弦的，则I(C‾)在所有域上都有线性分辨。逆序最近被拒绝了，但以下提出逆序的较弱版本的问题仍然悬而未决：如果I(C‾)有线性商，C必然是弦的吗？在这里，通过引入杂乱上升的概念，我们将这个问题分成两个更简单的问题，并提供一些线索来支持肯定的答案。特别地，我们证明了如果I(C‾)是具有顶点可分解Alexander对偶的单纯形复形的Stanley-Reisner理想，则C是弦的。
In this paper, we consider the generalization of chordal graphs to clutters proposed by Bigdeli, et al.(2017) in [2]. Assume that C 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‾) has linear quotients, is C 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‾) is the Stanley-Reisner ideal of a simplicial complex with a vertex decomposable Alexander dual, then C is chordal.