Robert Barritz

Distance-Eight SI-Orderings in Graphic and Cographic Matroids

We give a computer-assisted proof that two bases of a graphic or cographic matroid admit a subsequence-interchange ordering whenever their distance is at most eight. Consequently every graphic or cographic matroid of rank or corank at most eight is subsequence-interchangeably bas...

Proximity with Six Forbidden Basis Sums in Binary Matroids

Let the elements of a finite matroid be labeled by an arbitrary abelian group, and forbid a finite set F of possible basis sums. We give a computer-assisted proof that, in a binary matroid, if an avoiding basis exists, then every basis is within |F| exchanges of an avoiding basis...