Notes on the roots of Ehrhart polynomials
| dc.creator | Bey, Christian | |
| dc.creator | Henk, Martin | |
| dc.creator | Wills, Joerg M. | |
| dc.date | 2006-06-04 | |
| dc.date.accessioned | 2026-07-07T07:14:46Z | |
| dc.date.available | 2026-07-07T07:14:46Z | |
| dc.description | We determine lattice polytopes of smallest volume with a given number of interior lattice points. We show that the Ehrhart polynomials of those with one interior lattice point have largest roots with norm of order n^2, where n is the dimension. This improves on the previously best known bound n and complements a recent result of Braun where it is shown that the norm of a root of an Ehrhart polynomial is at most of order n^2. For the class of 0-symmetric lattice polytopes we present a conjecture on the smallest volume for a given number of interior lattice points and prove the conjecture for crosspolytopes. We further give a characterisation of the roots of the Ehrhart polyomials in the 3-dimensional case and we classify for n\leq 4 all lattice polytopes whose roots of their Ehrhart polynomials have all real part -1/2. These polytopes belong to the class of reflexive polytopes. | |
| dc.identifier | https://arxiv.org/abs/math/0606089 | |
| dc.identifier | http://arxiv.org/abs/math/0606089 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/113019 | |
| dc.subject | Metric Geometry | |
| dc.subject | Combinatorics | |
| dc.subject | 52C07; 11H06 | |
| dc.title | Notes on the roots of Ehrhart polynomials | |
| dc.type | text |