Ehrhart positivity for a certain class of panhandle matroids

TL;DR

This paper provides a combinatorial formula for Ehrhart coefficients of specific weighted multi-hypersimplices and proves their positivity in the case of panhandle matroids, advancing understanding of their geometric and combinatorial properties.

Contribution

It introduces a new combinatorial formula for Ehrhart coefficients and establishes their positivity for a class of panhandle matroids.

Findings

Ehrhart coefficients are positive for the considered class of panhandle matroids.

A combinatorial formula for these coefficients is derived.

The results connect polytope geometry with matroid theory.

Abstract

We give a combinatorial formula for the Ehrhart coefficients of a certain class of weighted multi-hypersimplices. In a special case, where these polytopes coincide with the base polytope of the panhandle matroid $\textrm{Pan}_{k,n-2,n}$, we show that the Ehrhart coefficients are positive.