Interlacing Ehrhart polynomials of reflexive polytopes

Akihiro Higashitani ^[1] ; Mario Kummer ^[2] ; Mateusz Michałek ^[2]
1. [1] Kyoto Sangyo University
  
  Kyoto Sangyo University
  
  Kamigyō-ku, Japón
2. [2] Max Planck Institute for Mathematics in the Sciences
  
  Max Planck Institute for Mathematics in the Sciences
  
  Kreisfreie Stadt Leipzig, Alemania
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 23, Nº. 4, 2017, págs. 2977-2998
Idioma: inglés
DOI: 10.1007/s00029-017-0350-6
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Resumen
- It was observed by Bump et al. that Ehrhart polynomials in a special family exhibit properties shared by 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.