Alexander Engström: Refined Ehrhart polynomials and an h*-triangle

Abstract

I will discuss some current work with Florian Kohl on a refinement of the Ehrhart polynomial of a polytope: ehr(s,t). For the corresponding generating function, we get a triangle of h*-coefficients instead of a vector and we prove that they are non-negative. Sometimes both s=1 and s=2 turns the refined Ehrhart polynomial into an ordinary one, as for example for stable set polytopes of perfect graphs and their associated reflexive polytopes. We state some conjectures on the h*-triangle.