descriptionPublicationkeyboard_double_arrow_right Article 01 Nov 2015 English Publisher:Elsevier BVJournal:European Journal of Combinatorics, volume 50, pages 18-29 (issn: 0195-6698,

Authors: Bonin, Joseph; Mier Vinué, Anna de;

doi: 10.1016/j.ejc.2015.03.011

handle: 2117/77053

Extensions and presentations of transversal matroids

- Summary
- Subjects
- Metrics

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. 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. Peer Reviewed

Related Organizations

Universitat Politècnica de Catalunya
Spain
Universitat Polite`cnica de Catalunya
Spain
George Washington University
United States

Keywords

stochastic geometry, :Matemàtiques i estadística::Matemàtica discreta::Combinatòria [Àrees temàtiques de la UPC], Combinatorial aspects of matroids and geometric lattices, random sets, independent sets, Transversal (matching) theory, Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria, Classificació AMS::60 Probability theory and stochastic processes::60D05 Geometric probability, stochastic geometry, random sets, :60 Probability theory and stochastic processes::60D05 Geometric probability, stochastic geometry, random sets [Classificació AMS], Probabilitats, Classificació AMS::60 Probability theory and stochastic processes::60D05 Geometric probability, transversal extensions, Geometric probabilities

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	2
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Average
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Average
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average