Ehrhart polynomials with negative coefficients

Takayuki Hibi, Akihiro Higashitani, Akiyoshi Tsuchiya, Koutarou Yoshida

Published 2013-12-26, updated 2013-12-31Version 3

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