Roots of Ehrhart polynomials of smooth Fano polytopes

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Hegedüs, Gábor and Kasprzyk, Alexander M. (2011) Roots of Ehrhart polynomials of smooth Fano polytopes. Discrete & Computational Geometry, 46 (3). pp. 488-499. ISSN 1432-0444

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Official URL: http://link.springer.com/article/10.1007%2Fs00454-010-9275-y

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.

Item Type:

Article

RIS ID:

https://nottingham-repository.worktribe.com/output/1009627

Keywords:

Lattice polytope, Ehrhart polynomial, Nonsingular toric Fano, Canonical line hypothesis

Schools/Departments:

University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences

Identification Number:

https://doi.org/10.1007/s00454-010-9275-y

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