The NF-Number of a Simplicial Complex

IF 0.4 4区数学 Q4 MATHEMATICS

Algebra Colloquium Pub Date : 2022-12-01 DOI:10.1142/s1005386722000451

T. Hibi, H. Mahmood

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引用次数: 1

Abstract

Let [Formula: see text] be a simplicial complex on [Formula: see text]. The [Formula: see text]-complex of [Formula: see text] is the simplicial complex [Formula: see text] on [Formula: see text] for which the facet ideal of [Formula: see text] is equal to the Stanley–Reisner ideal of [Formula: see text]. Furthermore, for each [Formula: see text], we introduce the [Formula: see text]th [Formula: see text]-complex [Formula: see text], which is inductively defined as [Formula: see text] by setting [Formula: see text]. One can set [Formula: see text]. The [Formula: see text]-number of [Formula: see text] is the smallest integer [Formula: see text] for which [Formula: see text]. In the present paper we are especially interested in the [Formula: see text]-number of a finite graph, which can be regraded as a simplicial complex of dimension one. It is shown that the [Formula: see text]-number of the finite graph [Formula: see text] on [Formula: see text], which is the disjoint union of the complete graphs [Formula: see text] on [Formula: see text] and [Formula: see text] on [Formula: see text] for [Formula: see text] and [Formula: see text] with [Formula: see text], is equal to [Formula: see text]. As a corollary, we find that the [Formula: see text]-number of the complete bipartite graph [Formula: see text] on [Formula: see text] is also equal to [Formula: see text].

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单纯复合体的nf数

设[公式:见文]为[公式:见文]的简单复合体。[公式:见文]的[公式:见文]复合体是[公式:见文]上的简单复合体[公式:见文]，其中[公式:见文]的面理想等于[公式:见文]的Stanley-Reisner理想。进一步，对于每一个[公式:见文]，我们引入[公式:见文]th[公式:见文]-complex[公式:见文]，通过设置[公式:见文]归纳定义为[公式:见文]。可以设置[公式:见正文]。[公式:见文]-[公式:见文]的数是[公式:见文]的最小整数[公式:见文]。在本文中，我们特别感兴趣的是一个有限图的[公式:见文本]-数，它可以回归为一个维数为1的简单复形。结果表明，对于[公式:见文]和[公式:见文]，[公式:见文]和[公式:见文]的完全图[公式:见文]与[公式:见文]的完全图[公式:见文]和[公式:见文]的完全图[公式:见文]的不相交数[公式:见文]等于[公式:见文]。作为推论，我们发现[公式:见文]上的[公式:见文]-完全二部图[公式:见文]的数也等于[公式:见文]。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Algebra Colloquium 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

625

审稿时长

15.6 months

期刊介绍： Algebra Colloquium is an international mathematical journal founded at the beginning of 1994. It is edited by the Academy of Mathematics & Systems Science, Chinese Academy of Sciences, jointly with Suzhou University, and published quarterly in English in every March, June, September and December. Algebra Colloquium carries original research articles of high level in the field of pure and applied algebra. Papers from related areas which have applications to algebra are also considered for publication. This journal aims to reflect the latest developments in algebra and promote international academic exchanges.