Matroids and their Dressians

TL;DR

This paper explores the structure of Dressians of matroids through initial matroids, introduces an efficient algorithm for their computation, and provides counterexamples to certain assumptions about matroid subdivisions.

Contribution

It presents a new algorithm for computing Dressians of matroids and applies it to various cases, advancing understanding of matroid subdivisions.

Findings

Algorithm for Dressian computation implemented and tested

Counterexamples to some conjectures about matroid subdivisions

Application to a range of interesting matroids

Abstract

We study Dressians of matroids using the initial matroids of Dress and Wenzel. These correspond to cells in regular matroid subdivisions of matroid polytopes. An efficient algorithm for computing Dressians is presented, and its implementation is applied to a range of interesting matroids. We give counterexamples to a few plausible statements about matroid subdivisions.