Universal inequalities in Ehrhart theory

Abstract

In this paper, we show the existence of universal inequalities for the h*-vector of a lattice polytope P, that is, we show that there are relations among the coefficients of the h*-polynomial that are independent of both the dimension and the degree of P. More precisely, we prove that the coefficients h* 1 and h* 2 of the h*-vector (h* 0, h* 1,..., h* d) of a lattice polytope of any degree satisfy Scott’s inequality if h* 3 = 0.