Extensions and presentations of transversal matroids

A transversal matroid M can be represented by a collection of sets, called a presentation of M, whose partial transversals are the independent sets of M. Minimal presentations are those for which removing any element from any set gives a presentation of a different matroid. We study the connections...

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Veröffentlicht in:European journal of combinatorics Jg. 50; S. 18 - 29
Hauptverfasser: Bonin, Joseph E., de Mier, Anna
Format: Journal Article Verlag
Sprache:Englisch
Veröffentlicht: Elsevier Ltd 01.11.2015
Schlagworte:
60 Probability theory and stochastic processes
60D05 Geometric probability, stochastic geometry, random sets
Classificació AMS
Combinatòria
Geometric probabilities
Matemàtica discreta
Matemàtiques i estadística
Probabilitats
Àrees temàtiques de la UPC
ISSN:0195-6698, 1095-9971
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Zusammenfassung:A transversal matroid M can be represented by a collection of sets, called a presentation of M, whose partial transversals are the independent sets of M. 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 M and extensions of presentations of M. We show that a presentation of M is minimal if and only if different extensions of it give different extensions of M; also, all transversal extensions of M can be obtained by extending the minimal presentations of M. We also begin to explore the partial order that the weak order gives on the transversal extensions of M.
ISSN:0195-6698
1095-9971
DOI:10.1016/j.ejc.2015.03.011