2026-04-14T04:10:06Zhttps://recercat.cat/oai/request

oai:recercat.cat:2117/781292026-01-24T03:25:28Zcom_2072_1033col_2072_452950

Completion and decomposition of a clutter into representable matroids Martí Farré, Jaume Mier Vinué, Anna de 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 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 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. Peer Reviewed Postprint (author’s final draft) 2015-05-01 Article Martí-Farré, J., De Mier, A. Completion and decomposition of a clutter into representable matroids. "Linear algebra and its applications", 01 Maig 2015, vol. 472, p. 31-47. 0024-3795 https://hdl.handle.net/2117/78129 10.1016/j.laa.2015.01.023 eng http://www.sciencedirect.com/science/article/pii/S002437951500052X http://creativecommons.org/licenses/by-nc-nd/3.0/es/ Open Access 17 p. application/pdf Elsevier