Counterexamples of the conjecture on roots of Ehrhart polynomials

Akihiro Higashitani

Counterexamples of the conjecture on roots of Ehrhart polynomials

Combinatorics 2011-06-29 v2

Authors: Akihiro Higashitani

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

Keywords

Ehrhart polynomial roots conjecture counterexamples integral convex polytope real part bound

Cite

@article{arxiv.1106.4633,
  title  = {Counterexamples of the conjecture on roots of Ehrhart polynomials},
  author = {Akihiro Higashitani},
  journal= {arXiv preprint arXiv:1106.4633},
  year   = {2011}
}

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6 pages

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