Counterexamples of the conjecture on roots of Ehrhart polynomials

Akihiro Higashitani

Published 2011-06-23, updated 2011-06-28Version 2

An outstanding conjecture on roots of Ehrhart polynomials says that all roots $\alpha$ of the Ehrhart polynomial of an integral convex polytope of dimension $d$ satisfy $-d \leq \Re(\alpha) \leq d-1$. In this paper, we suggest some counterexamples of this conjecture.