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arXiv · 1612.07538

Interlacing Ehrhart Polynomials of Reflexive Polytopes

Akihiro Higashitani·Mario Kummer·Mateusz Michałek
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Abstract

It was observed by Bump et al. that Ehrhart polynomials in a special family exhibit properties similar to the Riemann ζ function. The construction was generalized by Matsui et al. to a larger family of reflexive polytopes coming from graphs. We prove several conjectures confirming when such polynomials have zeros on a certain line in the complex plane. Our main new method is to prove a stronger property called interlacing.

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Akihiro Higashitani, Mario Kummer, Mateusz Michałek. 2016-12-22. Interlacing Ehrhart Polynomials of Reflexive Polytopes. https://doi.org/10.1007/s00029-017-0350-6

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