Matchings in simplicial complexes, circuits and toric varieties
type: Item
instance of: scholarly article
title: Matchings in simplicial complexes, circuits and toric varieties
zbMATH Open document ID: 1115.13029
author: Anargyros Katsabekis
author: Apostolos Thoma
published in: Journal of Combinatorial Theory. Series A
publication date: 2007-02-26T00:00:00Z
review text: The authors introduced a generalized notion of matching in a simplicial complex, called \(J\)-matching, and use it to define certain combinatorial invariants of the complex. Recently in [\textit{A. Katsabekis, M. Morales} and \textit{A. Thoma}, J. Pure Appl. Algebra 204, No. 3, 584--601 (2006; Zbl 1094.13035)], to any lattice ideal it was associated a cone \(\sigma \) and a simplicial complex \(D_\sigma \), with vertices the minimal non faces of \(\sigma \), as it was shown there combinatorial invariants of \(D_\sigma \) provides bounds for the minimal number of equations needed to described set theoretically an algebraic set: \(\text{ara}(V)\). The main object of the paper under review consists in giving lower bounds for \(\text{ara}(V)\) in terms of matching and other combinatorial numbers, for this the authors study first the properties of the generalized notion of matching.
Mathematics Subject Classification ID: 13F55
Mathematics Subject Classification ID: 14M25
zbMATH DE Number: 5129733
zbMATH Keywords: lattice ideals
zbMATH Keywords: arithmetical rank
zbMATH Keywords: matching
zbMATH Keywords: simplicial complex
reviewed by: Marcel Morales
describes a project that uses: CoCoA
MaRDI profile type: Publication
full work available at URL: j.jcta.2006.05.005
OpenAlex ID: W2108709862
cites work: An algorithm for the chromatic number of a graph
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cites work: Binomial ideals
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DOI: 10.1016/J.JCTA.2006.05.005
description: scientific article; zbMATH DE number 5129733