Counterexamples of the conjecture on roots of Ehrhart polynomials

Details Counterexamples of the conjecture on roots of Ehrhart polynomials Counterexamples of the conjecture on roots of Ehrhart polynomials

2011-06-23

arxiv.org/abs/1106.4633v2

Mathematics

Combinatorics

6 pages

Scientific paper

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.

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