Additive number theory and inequalities in Ehrhart theory (Q2800177)

In this paper, the author studies connections between Ehrhart theory and additive number theory. Further, he uses it to produce various inequalities between the coefficients of the \(h^\ast\)-polynomial of a lattice polytope (for the corresponding generating function). In particular, this improves some known classes of inequalities. For the case of dimension less than or equal to 6, this provides all ``balanced'' inequalities between the coefficients of the \(h^\ast\)-polynomial of a lattice polytope with an interior lattice point.