Computing Excluded Minors for Classes of Matroids Representable over Partial Fields

Abstract

We describe an implementation of a computer search for the "small" excluded minors for a class of matroids representable over a partial field.  Using these techniques, we enumerate the excluded minors on at most 15 elements for both the class of dyadic matroids, and the class of 2-regular matroids.  We conjecture that there are no other excluded minors for the class of 2-regular matroids; whereas, on the other hand, we show that there is a 16-element excluded minor for the class of dyadic matroids.