A Regular Unimodular Triangulation of the Matroid Base Polytope

TL;DR

This paper presents the first regular unimodular triangulation for any matroid base polytope and extends this to integral generalized permutahedra, resolving a longstanding open question.

Contribution

It introduces the first known regular unimodular triangulation for all matroid base polytopes and extends the method to generalized permutahedra.

Findings

First regular unimodular triangulation for any matroid base polytope

Extension of triangulation to integral generalized permutahedra

Resolved the open question about unimodular covers for matroid base polytopes

Abstract

We produce the first regular unimodular triangulation of an arbitrary matroid base polytope. We then extend our triangulation to integral generalized permutahedra. Prior to this work it was unknown whether each matroid base polytope admitted a unimodular cover.