BIER SPHERES OF EXTREMAL VOLUME AND GENERALIZED PERMUTOHEDRA
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 s...
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| Veröffentlicht in: | Applicable analysis and discrete mathematics 2023-04, Vol.17 (1), p.101-119 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | 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. |
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| ISSN: | 1452-8630 2406-100X |
| DOI: | 10.2298/AADM211010026J |