Matroids from hypersimplex splits

TL;DR

This paper introduces a broad class of matroids called split matroids, which include paving matroids, and explores their polyhedral and tropical geometric properties, leading to new insights into tropical Grassmannians.

Contribution

It defines split matroids, a large class extending paving matroids, and applies polyhedral geometry techniques to derive new results in tropical geometry.

Findings

Split matroids form a large class including all paving matroids.

Polyhedral techniques reveal structural properties of split matroids.

New results on the rays of tropical Grassmannians are obtained.

Abstract

A class of matroids is introduced which is very large as it strictly contains all paving matroids as special cases. As their key feature these split matroids can be studied via techniques from polyhedral geometry. It turns out that the structural properties of the split matroids can be exploited to obtain new results in tropical geometry, especially on the rays of the tropical Grassmannians.