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{\bf Joseph E. Bonin, Joseph P. S. Kung and Anna de Mier}
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{\bf Characterizations of Transversal and Fundamental Transversal Matroids}
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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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