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...
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Springer-Verlag
2011
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| Online Access: | https://eprints.nottingham.ac.uk/30735/ |
| _version_ | 1848794047009783808 |
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| author | Hegedüs, Gábor Kasprzyk, Alexander M. |
| author_facet | Hegedüs, Gábor Kasprzyk, Alexander M. |
| author_sort | Hegedüs, Gábor |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T19:09:58Z |
| format | Article |
| id | nottingham-30735 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:09:58Z |
| publishDate | 2011 |
| publisher | Springer-Verlag |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-307352020-05-04T20:23:05Z https://eprints.nottingham.ac.uk/30735/ Roots of Ehrhart polynomials of smooth Fano polytopes Hegedüs, Gábor Kasprzyk, Alexander M. 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. Springer-Verlag 2011-10 Article PeerReviewed 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 Lattice polytope Ehrhart polynomial Nonsingular toric Fano Canonical line hypothesis http://link.springer.com/article/10.1007%2Fs00454-010-9275-y doi:10.1007/s00454-010-9275-y doi:10.1007/s00454-010-9275-y |
| spellingShingle | Lattice polytope Ehrhart polynomial Nonsingular toric Fano Canonical line hypothesis Hegedüs, Gábor Kasprzyk, Alexander M. Roots of Ehrhart polynomials of smooth Fano polytopes |
| title | Roots of Ehrhart polynomials of smooth Fano polytopes |
| title_full | Roots of Ehrhart polynomials of smooth Fano polytopes |
| title_fullStr | Roots of Ehrhart polynomials of smooth Fano polytopes |
| title_full_unstemmed | Roots of Ehrhart polynomials of smooth Fano polytopes |
| title_short | Roots of Ehrhart polynomials of smooth Fano polytopes |
| title_sort | roots of ehrhart polynomials of smooth fano polytopes |
| topic | Lattice polytope Ehrhart polynomial Nonsingular toric Fano Canonical line hypothesis |
| url | https://eprints.nottingham.ac.uk/30735/ https://eprints.nottingham.ac.uk/30735/ https://eprints.nottingham.ac.uk/30735/ |