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arXiv · 1004.3817

Roots of Ehrhart Polynomials of Smooth Fano Polytopes

Gábor Hegedüs·Alexander M. Kasprzyk
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Abstract

V. Golyshev conjectured that for any smooth polytope P of dimension at most five, the roots $z\in\C$ of the Ehrhart polynomial for P have real part equal to -1/2. An elementary proof is given, and in each dimension the roots are described explicitly. We also present examples which demonstrate that this result cannot be extended to dimension six.

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Gábor Hegedüs, Alexander M. Kasprzyk. 2010-04-21. Roots of Ehrhart Polynomials of Smooth Fano Polytopes. https://doi.org/10.1007/s00454-010-9275-y

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