Lower bounds on the coefficients of Ehrhart polynomials

Martin Henk; Makoto Tagami

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arXiv · 0710.2665

Lower bounds on the coefficients of Ehrhart polynomials

Martin Henk·Makoto Tagami

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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.

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Martin Henk, Makoto Tagami. 2008-02-26. Lower bounds on the coefficients of Ehrhart polynomials. https://arxiv.org/abs/0710.2665

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