Lower bounds on the coefficients of Ehrhart polynomials

@article{Henk2009LowerBO,
title={Lower bounds on the coefficients of Ehrhart polynomials},
author={Martin Henk and Makoto Tagami},
journal={Eur. J. Comb.},
year={2009},
volume={30},
pages={70-83}
}

We present lower bounds for the coefficients of Ehrhart polynomials of convex lattice polytopes in terms of their volume. We also introduce two formulas for calculating the Ehrhart series of a kind of a ”weak” free sum of two lattice polytopes and of integral dilates of a polytope. As an application of these formulas we show that Hibi’s lower bound on the coefficients of the Ehrhart series is not true for lattice polytopes without interior lattice points.