%0 Journal Article
%T Additive number theory and inequalities in Ehrhart theory
%A Alan Stapledon
%J Mathematics
%D 2009
%I arXiv
%X We introduce a powerful connection between Ehrhart theory and additive number theory, and use it to produce infinitely many new classes of inequalities between the coefficients of the $h^*$-polynomial of a lattice polytope. This greatly improves upon the three known classes of inequalities, which were proved using techniques from commutative algebra and combinatorics. As an application, we deduce all possible `balanced' inequalities between the coefficients of the $h^*$-polynomial of a lattice polytope containing an interior lattice point, in dimension at most 6.
%U http://arxiv.org/abs/0904.3035v2