Gabriele Balletti: Universal inequalities in Ehrhart Theory

Abstract

Characterizing the h^*-polynomials of lattice polytopes is an incredibly hard business. Luckily in the last decades some relations among the coefficients of h^*-vectors have been proved, and all of them have some dependence either on the degree or the dimension of the lattice polytopes. In a recent work with A. Higashitani we prove that this is not always the case, by proving a relation which is "universal". In particular we prove that Scott's inequality is true in each dimension and degree, if interpreted correctly.