Interlacing Ehrhart polynomials of reflexive polytopes

Type of Publication: Journal article
Publication status: Published
URI (citable link): http://nbn-resolving.de/urn:nbn:de:bsz:352-2-6gysffozeawt9
Author: Higashitani, Akihiro; Kummer, Mario; Michalek, Mateusz
Year of publication: 2017
Published in: Selecta Mathematica ; 23 (2017), 4. - pp. 2977-2998. - Birkhäuser bei Springer. - ISSN 1022-1824. - eISSN 1420-9020
DOI (citable link): https://dx.doi.org/10.1007/s00029-017-0350-6
Summary:
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.
Subject (DDC): 510 Mathematics
Link to License: Attribution 4.0 International
Refereed: Yes

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HIGASHITANI, Akihiro, Mario KUMMER, Mateusz MICHALEK, 2017. Interlacing Ehrhart polynomials of reflexive polytopes. In: Selecta Mathematica. Birkhäuser bei Springer. 23(4), pp. 2977-2998. ISSN 1022-1824. eISSN 1420-9020. Available under: doi: 10.1007/s00029-017-0350-6

@article{Higashitani2017-10Inter-52564, title={Interlacing Ehrhart polynomials of reflexive polytopes}, year={2017}, doi={10.1007/s00029-017-0350-6}, number={4}, volume={23}, issn={1022-1824}, journal={Selecta Mathematica}, pages={2977--2998}, author={Higashitani, Akihiro and Kummer, Mario and Michalek, Mateusz} }

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