Roots of Ehrhart polynomials of smooth Fano polytopes

Heged�s, G�bor; Kasprzyk, Alexander M.

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.

Citation

Hegedüs, G., & Kasprzyk, A. M. (2011). Roots of Ehrhart polynomials of smooth Fano polytopes. Discrete and Computational Geometry, 46(3), https://doi.org/10.1007/s00454-010-9275-y

• Journal Article Type: Article
• Publication Date: Oct 1, 2011
• Deposit Date: Nov 12, 2015
• Publicly Available Date: Nov 12, 2015
• Journal: Discrete & Computational Geometry
• Print ISSN: 0179-5376
• Electronic ISSN: 1432-0444
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 46
• Issue: 3
• DOI: https://doi.org/10.1007/s00454-010-9275-y
• Keywords: Lattice polytope, Ehrhart polynomial, Nonsingular toric Fano, Canonical line hypothesis
• Public URL: https://nottingham-repository.worktribe.com/output/1009627
• Publisher URL: http://link.springer.com/article/10.1007%2Fs00454-010-9275-y
• Related Public URLs: http://link.springer.com/journal/454