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.

21 pages, 3 figures

References in corpus (7)

• Confinement of matroid representations to subsets of partial fields
• Computer-verification of the structure of some classes of fragile matroids
• The excluded minors for 2- and 3-regular matroids
• $N$-detachable pairs in 3-connected matroids III: the theorem
• Excluded minors are almost fragile
• Excluded minors are almost fragile II: essential elements
• Lift theorems for representations of matroids over pastures

Cited by in corpus (1)

• The excluded minors for GF(5)-representable matroids on ten elements