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
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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.