Bier spheres of extremal volume and generalized permutohedra

IF 1 4区数学 Q1 MATHEMATICS

Applicable Analysis and Discrete Mathematics Pub Date : 2021-08-02 DOI:10.2298/aadm211010026j

Filip D. Jevti'c, Rade T. vZivaljevi'c

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.

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极值体积的Bier球与广义置换面体

我们研究了Bier球的隐几何Bier(K) = K * ?K ?通过描述它们的自然几何实现，计算它们的体积，描述它们的多面性的有效准则，并将Bier(K)与Braid扇的自然粗化扇(K)联系起来。我们还建立了最大体积Bier球与经典Van Kampen-Flores定理的最新推广之间的联系，并阐明了Bier球在广义复面体理论中的作用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applicable Analysis and Discrete Mathematics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.40

自引率

11.10%

发文量

审稿时长

>12 weeks

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/).