Finding optimal minors of valuated bimatroids Original Research Article

As a variant of “valuated matroid” of Dress and Wenzel, we define the concept of a “valuated bimatroid” to investigate the combinatorial properties of the degree of subdeterminants of a rational function matrix. Two algorithms are developed for computing the maximum degree of a minor of specified order; the algorithms are valid also for “valuated bimatroids” in general.