Lower bounds on the coefficients of Ehrhart polynomials

• DOI: 10.1016/j.ejc.2008.02.009
• Publication Date: 2008-04-21T20:33:06Z
• Authors: Martin Henk; Makoto Tagami
• Keywords: Metric Geometry (math.MG); 52B20; 0102 computer and information sciences; 01 natural sciences; Theoretical Computer Science; Computational Theory and Mathematics; Mathematics - Metric Geometry; 52C07; FOS: Mathematics; Mathematics - Combinatorics; Geometry and Topology; Combinatorics (math.CO); 0101 mathematics; 52C07; 11H06; 52B20; 11H06

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