Linearly dependent vectorial decomposition of clutters

This paper deals with the question of completing a monotone increasing family of subsets of a finite set to obtain the linearly dependent subsets of a family of vectors of a vector space. Specifically, we demonstrate that such vectorial completions of the family of subsets ¿ exist and, in addition,...

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Detalles Bibliográficos
Autor: Martí Farré, Jaume|||0000-0002-2596-5971
Tipo de recurso: artículo
Fecha de publicación:2014
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/27361
Acceso en línea:https://hdl.handle.net/2117/27361
https://dx.doi.org/10.1016/j.endm.2014.08.028
Access Level:acceso abierto
Palabra clave:Clutter
Antichain
Hypergraph
Matroid
Decomposition.
Classificació AMS::05 Combinatorics
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria
Descripción
Sumario:This paper deals with the question of completing a monotone increasing family of subsets of a finite set to obtain the linearly dependent subsets of a family of vectors of a vector space. Specifically, we demonstrate that such vectorial completions of the family of subsets ¿ exist and, in addition, we show that the minimal vectorial completions of the family ¿ provide a decomposition of the clutter of the inclusion-minimal elements of ¿. The computation of such vectorial decomposition of clutters is also discussed in some cases.