Characterizations of transversal and fundamental transversal matroids

Details Characterizations of transversal and fundamental transversal matroids Characterizations of transversal and fundamental transversal matroids

2010-09-17

arxiv.org/abs/1009.3435v1

Mathematics

Combinatorics

12 pages, 1 figure

Scientific paper

A result of Mason, as refined by Ingleton, characterizes transversal matroids as the matroids that satisfy a set of inequalities that relate the ranks of intersections and unions of nonempty sets of cyclic flats. We prove counterparts, for fundamental transversal matroids, of this and other characterizations of transversal matroids. In particular, we show that fundamental transversal matroids are precisely the matroids that yield equality in Mason's inequalities and we deduce a characterization of fundamental transversal matroids due to Brylawski from this simpler characterization.

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