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Counterexamples of the Conjecture on Roots of Ehrhart Polynomials

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On roots of Ehrhart polynomials, Beck et al. conjecture that all roots α of the Ehrhart polynomial of an integral convex polytope of dimension d satisfy −d≤ℜ(α)≤d−1. In this paper, we provide counterexamples for this conjecture.


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Correspondence to Akihiro Higashitani.

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Higashitani, A. Counterexamples of the Conjecture on Roots of Ehrhart Polynomials. Discrete Comput Geom 47, 618–623 (2012). https://doi.org/10.1007/s00454-011-9390-4

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  • Integral convex polytope
  • Ehrhart polynomial
  • δ-vector