Counterexamples of the conjecture on roots of Ehrhart polynomials

Abstract

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 $-d\le \Re (\alpha )\le d-1$. In this paper, we suggest some counterexamples of this conjecture.

6 pages