Interlacing Ehrhart Polynomials of Reflexive Polytopes
Akihiro Higashitani, Mario Denis Kummer, and Mateusz Michałek
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Submission date: 09. Jan. 2017
published in: Selecta mathematica, 23 (2017) 4, p. 2977-2998
DOI number (of the published article): 10.1007/s00029-017-0350-6
Link to arXiv: See the arXiv entry of this preprint.
It was observed by Bump et al. that Ehrhart polynomials in a special family exhibit properties similar to the Riemann zeta 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.