2006/02/06 by Sonja Lj. Cukic, Sonja Lj. Čukić, Cukic, Sonja Lj. +2
Computer Science · Mathematics · #06A07 #52B22 #55U10 #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric and Algebraic Topology #Topological and Geometric Data Analysis #math.CO #msc:06A07 #msc:52B22 #msc:55U10
paper · pdf · doi:10.48550/arxiv.math/0602101
11 pages, 3 figures
arxiv created 2006/02/06 · openalex publication_date 2006/02/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The construction of the Bier sphere Bier(K) for a simplicial complex K is due to Bier. Björner, Paffenholz, Sjöstrand and Ziegler generalize this construction to obtain a Bier poset Bier(P,I) from any bounded poset P and any proper ideal I of P. They show shellability of Bier(P,I) for the case where P is the boolean lattice, and obtain thereby 'many shellable spheres' in the sense of Kalai. We put the Bier construction into the general framework of the theory of nested set complexes of Feichtner and Kozlov. We obtain 'more shellable spheres' by proving the general statement that combinatorial blowups, hence stellar subdivisions, preserve shellability.