English

Lower bounds on the coefficients of Ehrhart polynomials

Metric Geometry 2008-02-26 v2 Combinatorics

Abstract

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.

Keywords

Cite

@article{arxiv.0710.2665,
  title  = {Lower bounds on the coefficients of Ehrhart polynomials},
  author = {Martin Henk and Makoto Tagami},
  journal= {arXiv preprint arXiv:0710.2665},
  year   = {2008}
}

Comments

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

R2 v1 2026-06-21T09:31:31.031Z