Hidefumi Ohsugi ; Kazuki Shibata - Smooth Fano polytopes whose Ehrhart polynomial has a root with large real part

dmtcs:3041 - Discrete Mathematics & Theoretical Computer Science, January 1, 2012, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) - https://doi.org/10.46298/dmtcs.3041
Smooth Fano polytopes whose Ehrhart polynomial has a root with large real partArticle

Authors: Hidefumi Ohsugi 1; Kazuki Shibata 1

  • 1 Department of Mathematics [Rikkyo]

The symmetric edge polytopes of odd cycles (del Pezzo polytopes) are known as smooth Fano polytopes. In this extended abstract, we show that if the length of the cycle is 127, then the Ehrhart polynomial has a root whose real part is greater than the dimension. As a result, we have a smooth Fano polytope that is a counterexample to the two conjectures on the roots of Ehrhart polynomials.

https://doi.org/10.46298/dmtcs.3041
Source: HAL:hal-01283170v1
Volume: DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
Section: Proceedings
Published on: January 1, 2012
Imported on: January 31, 2017
Keywords: Ehrhart polynomials, Grôbner bases, Gorenstein Fano polytopes.,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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