Universal inequalities in Ehrhart Theory

Abstract

In this paper, we show the existence of universal inequalities for the $h^{\ast }$-vector of a lattice polytope P, that is, we show that there are relations among the coefficients of the $h^{\ast }$-polynomial which are independent of both the dimension and the degree of P. More precisely, we prove that the coefficients $h_1^{\ast }$ and $h_2^{\ast }$ of the $h^{\ast }$-vector $(h_0^{\ast },h_1^{\ast },\dots ,h_d^{\ast })$ of a lattice polytope of any degree satisfy Scott's inequality if $h_3^{\ast }=0$.

9 pages, 1 figure

References in corpus (1)

• A generalization of a theorem of G. K. White