Bimatroids and invariants

AbstractA bimatroid B between the sets S and T incorporates the combinatorial exchange properties of relative invariants of the special linear group acting on a vector space and its dual, or equivalently, when S and T are finite, the exchange properties fo nonsingular minors of a matrix whose columns and rows are indexed by S and T. A rather simple idea, basically that of adjoining an identity matrix, yields a construction which produces, from the bimatroid B, a matroid R on the disjoint union S ∪ T which encodes all the structure of B. This gives a method of translating matroidal concepts and results into the language of bimatroids. We also define an analog of matrix multiplication for bimatroids: This operation generalizes matroid induction and affords another combinatorial interpretation of a linear transformation