Extensions and presentations of transversal matroids

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To access the full text documents, please follow this link: http://hdl.handle.net/2117/77053

Title:	Extensions and presentations of transversal matroids
Author:	Bonin, Joseph; Mier Vinué, Anna de
Other authors:	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II; Universitat Politècnica de Catalunya. MD - Matemàtica Discreta
Abstract:	A transversal matroid MM can be represented by a collection of sets, called a presentation of MM, whose partial transversals are the independent sets of MM. Minimal presentations are those for which removing any element from any set gives a presentation of a different matroid. We study the connections between (single-element) transversal extensions of MM and extensions of presentations of MM. We show that a presentation of MM is minimal if and only if different extensions of it give different extensions of MM; also, all transversal extensions of MM can be obtained by extending the minimal presentations of MM. We also begin to explore the partial order that the weak order gives on the transversal extensions of MM.
Abstract:	A transversal matroid MM can be represented by a collection of sets, called a presentation of MM, whose partial transversals are the independent sets of MM. Minimal presentations are those for which removing any element from any set gives a presentation of a different matroid. We study the connections between (single-element) transversal extensions of MM and extensions of presentations of MM. We show that a presentation of MM is minimal if and only if different extensions of it give different extensions of MM; also, all transversal extensions of MM can be obtained by extending the minimal presentations of MM. We also begin to explore the partial order that the weak order gives on the transversal extensions of MM.
Abstract:	Peer Reviewed
Subject(s):	-Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria -Geometric probabilities -Probabilitats -Classificació AMS::60 Probability theory and stochastic processes::60D05 Geometric probability, stochastic geometry, random sets
Rights:	http://creativecommons.org/licenses/by-nc-nd/3.0/es/
Document type:	Article - Submitted version Article
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