| Authors: | Jevtić, Filip Živaljević, Rade |
Affiliations: | Mechanics Mathematical Institute of the Serbian Academy of Sciences and Arts |
Title: | BIER SPHERES OF EXTREMAL VOLUME AND GENERALIZED PERMUTOHEDRA | Journal: | Applicable Analysis and Discrete Mathematics | Volume: | 17 | Issue: | 1 | First page: | 101 | Last page: | 119 | Issue Date: | 2023 | Rank: | ~M21 | ISSN: | 1452-8630 | DOI: | 10.2298/AADM211010026J | Abstract: | We study hidden geometry of Bier spheres Bier(K) = K *Δ 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 |
Keywords: | Bier sphere | Braid fan | Generalized permutohedra | Van Kampen-Flores theorem | Publisher: | University of Belgrade, School of Electrical Engineering |
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