Corpus ID: 236772179

Bier spheres of extremal volume and generalized permutohedra

  title={Bier spheres of extremal volume and generalized permutohedra},
  author={Filip D. Jevti'c and Rade T. vZivaljevi'c},
A Bier sphere Bier(K) = K ∗∆ K◦, defined as the deleted join of a simplicial complex and its Alexander dual K◦, is a purely combinatorial object (abstract simplicial complex). Here we study a hidden geometry of Bier spheres by describing their natural geometric realizations, compute their volume, describe an effective criterion for their polytopality, and associate to K a natural fan Fan(K), related to the Braid fan. Along the way we establish a connection of Bier spheres of maximal volume with… Expand

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