Abstract
An algorithm is presented for determining whether or not a matroid is a transversal matroid. If the matroid is a transversal matroid, the algorithm furnishes an explicit determination of the maximal presentation (which therefore must be unique). From this we obtain necessary and sufficient conditions for a matroid to be a transversal matroid and two characterizations of the presentations of a given transversal matroid. We also evaluate the cardinalities of the members of presentations of a transversal matroid in terms of the cardinalities of the members of the maximal presentation and the ranks of the complements of each. Numerous other consequences are derived.
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