Interlacing Ehrhart polynomials of reflexive polytopes

Thumbnail Image
Files
Higashitani_2-6gysffozeawt9.pdf(578.96 KB)
Date
2017
Authors
Higashitani, Akihiro
Editors
Contact
Journal ISSN
Electronic ISSN
ISBN
Bibliographical data
Publisher
Series
URI (citable link)
urn:nbn:de:bsz:352-2-6gysffozeawt9
DOI (citable link)
10.1007/s00029-017-0350-6
ArXiv-ID
International patent number
Link to the license

CC BY 4.0

EU project number
Project
Open Access publication
Collections
Mathematik und Statistik
Restricted until
Title in another language
Research Projects
Organizational Units
Journal Issue
Publication type
Journal article
Publication status
Published
Published in
Selecta Mathematica ; 23 (2017), 4. - pp. 2977-2998. - BirkhΓ€user bei Springer. - ISSN 1022-1824. - eISSN 1420-9020
Abstract
It was observed by Bump et al. that Ehrhart polynomials in a special family exhibit properties shared by the Riemann ΞΆ 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.
Summary in another language
Subject (DDC)
510 Mathematics
Keywords
Conference
Review
undefined / . - undefined, undefined. - (undefined; undefined)
Cite This
ISO 690HIGASHITANI, Akihiro, Mario KUMMER, Mateusz MICHALEK, 2017. Interlacing Ehrhart polynomials of reflexive polytopes. In: Selecta Mathematica. BirkhΓ€user bei Springer. 23(4), pp. 2977-2998. ISSN 1022-1824. eISSN 1420-9020. Available under: doi: 10.1007/s00029-017-0350-6
BibTex
@article{Higashitani2017-10Inter-52564,
  year={2017},
  doi={10.1007/s00029-017-0350-6},
  title={Interlacing Ehrhart polynomials of reflexive polytopes},
  number={4},
  volume={23},
  issn={1022-1824},
  journal={Selecta Mathematica},
  pages={2977--2998},
  author={Higashitani, Akihiro and Kummer, Mario and Michalek, Mateusz}
}
RDF
<rdf:RDF
    xmlns:dcterms="http://purl.org/dc/terms/"
    xmlns:dc="http://purl.org/dc/elements/1.1/"
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:bibo="http://purl.org/ontology/bibo/"
    xmlns:dspace="http://digital-repositories.org/ontologies/dspace/0.1.0#"
    xmlns:foaf="http://xmlns.com/foaf/0.1/"
    xmlns:void="http://rdfs.org/ns/void#"
    xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > 
  <rdf:Description rdf:about="https://kops.uni-konstanz.de/server/rdf/resource/123456789/52564">
    <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/52564"/>
    <dcterms:rights rdf:resource="http://creativecommons.org/licenses/by/4.0/"/>
    <dcterms:hasPart rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/52564/1/Higashitani_2-6gysffozeawt9.pdf"/>
    <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2021-01-26T10:35:33Z</dcterms:available>
    <dcterms:issued>2017-10</dcterms:issued>
    <dc:contributor>Higashitani, Akihiro</dc:contributor>
    <dc:creator>Kummer, Mario</dc:creator>
    <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
    <dcterms:title>Interlacing Ehrhart polynomials of reflexive polytopes</dcterms:title>
    <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2021-01-26T10:35:33Z</dc:date>
    <dc:creator>Higashitani, Akihiro</dc:creator>
    <dcterms:abstract xml:lang="eng">It was observed by Bump et al. that Ehrhart polynomials in a special family exhibit properties shared by the Riemann ΞΆ 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.</dcterms:abstract>
    <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <foaf:homepage rdf:resource="http://localhost:8080/"/>
    <dspace:hasBitstream rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/52564/1/Higashitani_2-6gysffozeawt9.pdf"/>
    <dc:contributor>Kummer, Mario</dc:contributor>
    <dc:rights>Attribution 4.0 International</dc:rights>
    <dc:creator>Michalek, Mateusz</dc:creator>
    <dc:contributor>Michalek, Mateusz</dc:contributor>
    <dc:language>eng</dc:language>
  </rdf:Description>
</rdf:RDF>
Internal note
xmlui.Submission.submit.DescribeStep.inputForms.label.kops_note_fromSubmitter
Contact
URL of original publication
Test date of URL
Examination date of dissertation
Method of financing
Comment on publication
Alliance license
Corresponding Authors der Uni Konstanz vorhanden
International Co-Authors
Bibliography of Konstanz
No
Refereed
Yes