{"title":"Bier spheres of extremal volume and generalized permutohedra","authors":"Filip D. Jevti'c, Rade T. vZivaljevi'c","doi":"10.2298/aadm211010026j","DOIUrl":null,"url":null,"abstract":"We study hidden geometry of Bier spheres Bier(K) = K * ? K? by describing\n their natural geometric realizations, compute their volume, describe an\n effective criterion for their polytopality, and associate to Bier(K) a\n natural coarsening Fan(K) of the Braid fan. We also establish a connection\n of Bier spheres of maximal volume with recent generalizations of the\n classical Van Kampen-Flores theorem and clarify the role of Bier spheres in\n the theory of generalized permutohedra.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2021-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applicable Analysis and Discrete Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2298/aadm211010026j","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 2
Abstract
We study hidden geometry of Bier spheres Bier(K) = K * ? K? by describing
their natural geometric realizations, compute their volume, describe an
effective criterion for their polytopality, and associate to Bier(K) a
natural coarsening Fan(K) of the Braid fan. We also establish a connection
of Bier spheres of maximal volume with recent generalizations of the
classical Van Kampen-Flores theorem and clarify the role of Bier spheres in
the theory of generalized permutohedra.
期刊介绍：
Applicable Analysis and Discrete Mathematics is indexed, abstracted and cover-to cover reviewed in: Web of Science, Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES), Mathematical Reviews/MathSciNet, Zentralblatt für Mathematik, Referativny Zhurnal-VINITI. It is included Citation Index-Expanded (SCIE), ISI Alerting Service and in Digital Mathematical Registry of American Mathematical Society (http://www.ams.org/dmr/).
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