Ehrhart polynomials with negative coefficients

Abstract

It is shown that, for each $d\ge 4$, there exists an integral convex polytope $\mathcal{P}$ of dimension $d$ such that each of the coefficients of $n,n^2,\dots ,n^{d-2}$ of its Ehrhart polynomial $i(\mathcal{P},n)$ is negative.

4 pages