Extending simplicial complexes: Topological and combinatorial properties

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2024-11-27 DOI:10.1016/j.disc.2024.114335

Mohammad Farrokhi D.G. , Alireza Shamsian , Ali Akbar Yazdan Pour

引用次数: 0

Abstract

Given an arbitrary hypergraph

H

, we may glue to

H

a family of hypergraphs to get a new hypergraph

H^{'}

having

H

as an induced subhypergraph. In this paper, we introduce three gluing techniques for which the topological and combinatorial properties (such as Cohen-Macaulayness, shellability, vertex-decomposability etc.) of the resulting hypergraph

H^{'}

is under control in terms of the glued components. This enables us to construct broad classes of simplicial complexes containing a given simplicial complex as induced subcomplex satisfying nice topological and combinatorial properties. Our results will be accompanied with some interesting open problems.

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扩展简单复数：拓扑和组合特性

给定一个任意的超图 H，我们可以将一个超图族粘合到 H 上，从而得到一个以 H 为诱导子超图的新超图 H′。在本文中，我们介绍了三种粘合技术，其拓扑和组合特性（如科恩-马科拉伊性、可脱壳性、顶点可分解性等）都可以通过粘合成分来控制。这使我们能够构造出一大类简单复数，其中包含一个给定简单复数作为诱导子复数，并满足良好的拓扑和组合特性。我们的成果将伴随着一些有趣的开放性问题。

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

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.