Roots of Ehrhart polynomials of smooth Fano polytopes
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 t...
| Main Authors: | , |
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| Format: | Article |
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Springer-Verlag
2011
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| Online Access: | https://eprints.nottingham.ac.uk/30735/ |
| Summary: | 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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