Integer point enumeration on independence polytopes and half-open hypersimplices

Luis Ferroni

Published 2020-12-08Version 1

In this paper we investigate the Ehrhart Theory of the independence matroid polytope of uniform matroids. It is proved that these polytopes have an Ehrhart polynomial with positive coefficients. To do that, we prove that indeed all half-open-hypersimplices are Ehrhart positive, and tile disjointly our polytope using them.