The Erhart polynomials of matroids and hypersimplices
- Luis Ferroni (University of Bologna, Bologna, Italy)
The Ehrhart polynomial of a polytope counts the number of lattice points in every integer dilation of the polytope. A conjecture of De Loera et al. states that if the polytope is a matroid polytope, then these polynomials have positive coefficients. For uniform matroids it is indeed true, because in fact in that case the polytopes are hypersimplices. We will also discuss some purely matroidal operations that behave nicely with the Ehrhart polynomial of a matroid and discuss further conjectures and results on the matter.