Excluded minors for the class of split matroids

TL;DR

This paper characterizes the class of split matroids by identifying all minimal matroids that are not split, confirming a conjecture and advancing understanding of their structural properties.

Contribution

It provides the first complete excluded-minor characterization of split matroids, linking geometric and combinatorial definitions.

Findings

Identified all excluded minors for split matroids

Confirmed a conjecture by Joswig and Schröter

Bridged geometric and combinatorial perspectives on split matroids

Abstract

Split matroids form a minor-closed class of matroids, and are defined by placing conditions on the system of split hyperplanes in the matroid base polytope. They can equivalently be defined in terms of structural properties involving cyclic flats. We confirm a conjecture of Joswig and Schr\"{o}ter by proving an excluded-minor characterisation of the class of split matroids.