Bier Spheres of Extremal Volume and Generalized Permutohedra

Applicable Analysis and Discrete Mathematics

article

Filip D. Jevtić¹  Rade T. Živaljević¹ 

[1] Mathematical Institute, Serbian Academy of Sciences and Arts

关键词: Bier sphere;    Braid fan;    Generalized permutohedra;    Van Kampen-Flores theorem;   

DOI  :  10.2298/AADM211010026J

学科分类：社会科学、人文和艺术（综合）

来源: Univerzitet u Beogradu * Elektrotehnicki Fakultet / University of Belgrade, Faculty of Electrical Engineering

【 摘 要 】

We study hidden geometry of Bier spheres Bier(K) = K ∗∆ K◦ by describing their natural geometric realizations, compute their volume, describe aneffective criterion for their polytopality, and associate to Bier(K) a naturalcoarsening F an(K) of the braid fan. We also establish a connection of Bierspheres of maximal volume with recent generalizations of the classical VanKampen-Flores theorem and clarify the role of Bier spheres in the theory ofgeneralized permutohedra.

【 授权许可】

Unknown