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

Authors: Ohsugi, Hidefumi and Shibata, Kazuki

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.


Volume: DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
Section: Proceedings
Published on: January 1, 2012
Submitted on: January 31, 2017
Keywords: Ehrhart polynomials, Grôbner bases, Gorenstein Fano polytopes.,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]


Share

Consultation statistics

This page has been seen 58 times.
This article's PDF has been downloaded 228 times.