Facial structures of lattice path matroid polytopes

TL;DR

This paper investigates the facial structures of matroid base polytopes specifically associated with lattice path matroids, providing insights into their geometric and combinatorial properties.

Contribution

It offers a detailed analysis of the facial structures of lattice path matroid polytopes, a novel focus in the study of matroid base polytopes.

Findings

Characterization of facial structures of lattice path matroid polytopes

Identification of geometric properties specific to these polytopes

Insights into the combinatorial complexity of lattice path matroid polytopes

Abstract

A lattice path matroid is a transversal matroid corresponding to a pair of lattice paths on the plane. A matroid base polytope is the polytope whose vertices are the incidence vectors of the bases of the given matroid. In this paper, we study facial structures of matroid base polytopes corresponding to lattice path matroids.