Lower bounds on the coefficients of Ehrhart polynomials

Details Lower bounds on the coefficients of Ehrhart polynomials Lower bounds on the coefficients of Ehrhart polynomials

2007-10-14

arxiv.org/abs/0710.2665v2

Mathematics

Metric Geometry

v2: minor corrections; referees comments and suggestions incorporated. To appear in European J. Combinat

Scientific paper

We present lower bounds for the coefficients of Ehrhart polynomials of convex lattice polytopes in terms of their volume. Concerning the coefficients of the Ehrhart series of a lattice polytope we show that Hibi's lower bound is not true for lattice polytopes without interior lattice points. The counterexample is based on a formula of the Ehrhart series of the join of two lattice polytope. We also present a formula for calculating the Ehrhart series of integral dilates of a polytope.

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