Completion and decomposition of a clutter into representable matroids

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Title:	Completion and decomposition of a clutter into representable matroids
Author:	Martí Farré, Jaume; Mier Vinué, Anna de
Other authors:	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV; Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II; Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions; Universitat Politècnica de Catalunya. MD - Matemàtica Discreta
Abstract:	This paper deals with the question of completing a monotone increasing family of subsets Gamma of a finite set Omega to obtain the linearly dependent subsets of a family of vectors of a vector space. Specifically, we prove that such vectorial completions of the family of subsets Gamma exist and, in addition, we show that the minimal vectorial completions of the family Gamma provide a decomposition of the clutter Lambda of the inclusion-minimal elements of Gamma. The computation of such vectorial decomposition of clutters is also discussed in some cases. (C) 2015 Elsevier Inc. All rights reserved.
Abstract:	Peer Reviewed
Subject(s):	-Àrees temàtiques de la UPC::Matemàtiques i estadística::Probabilitat -Graph theory -Clutter -Hypergraph -Matroid -Decomposition -Representable matroid -Teoria de grafs -Classificació AMS::05 Combinatorics::05C Graph theory
Rights:	http://creativecommons.org/licenses/by-nc-nd/3.0/es/
Document type:	Article - Submitted version Article
Published by:	Elsevier
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