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arXiv · 1112.5777

Roots of Ehrhart polynomials and symmetric $δ$-vectors

Akihiro Higashitani
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Abstract

The conjecture on roots of Ehrhart polynomials, stated by Matsui et al. \cite[Conjecture 4.10]{MHNOH}, says that all roots $α$ of the Ehrhart polynomial of a Gorenstein Fano polytope of dimension $d$ satisfy $-\frac{d}{2} \leq \Re(α) \leq \frac{d}{2} -1$. In this paper, we observe the behaviors of roots of SSNN polynomials which are a wider class of the polynomials containing all the Ehrhart polynomials of Gorenstein Fano polytopes. As a result, we verify that this conjecture is true when the roots are real numbers or when $d \leq 5$.

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Akihiro Higashitani. 2012-11-15. Roots of Ehrhart polynomials and symmetric $δ$-vectors. https://arxiv.org/abs/1112.5777

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