Flag enumerations of matroid base polytopes

TL;DR

This paper investigates the combinatorial and geometric structures of matroid base polytopes, focusing on flag structures, face descriptions, hyperplane splits, and the cd-index, especially for rank 2 matroids.

Contribution

It provides new characterizations of faces and splits of matroid base polytopes and relates the cd-index to these structures, advancing understanding of their combinatorial properties.

Findings

Faces of matroid base polytopes are described in terms of matroid data.

Conditions for hyperplane splits of matroid base polytopes are established.

The cd-index of a matroid base polytope of rank 2 is explicitly expressed.

Abstract

In this paper, we study flag structures of matroid base polytopes. We describe faces of matroid base polytopes in terms of matroid data, and give conditions for hyperplane splits of matroid base polytopes. Also, we show how the cd-index of a polytope can be expressed when a polytope is split by a hyperplane, and apply these to the cd-index of a matroid base polytope of a rank 2 matroid.