2011/02/01 by Satoshi Murai, Eran Nevo, Murai, Satoshi +1
Computer Science · Mathematics · #05E45 #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #Digital Image Processing Techniques #FOS: Mathematics #Point processes and geometric inequalities #math.CO #msc:05E45
paper · pdf · doi:10.48550/arxiv.1102.0096
11 pages, no figures
arxiv created 2011/02/01 · openalex publication_date 2011/02/01 · arxiv updated 2011/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that the γ-vector of the order complex of any polytope is the f-vector of a balanced simplicial complex. This is done by proving this statement for a subclass of Stanley's S-shellable spheres which includes all polytopes. The proof shows that certain parts of the cd-index, when specializing c=1 and considering the resulted polynomial in d, are the f-polynomials of simplicial complexes that can be colored with "few" colors. We conjecture that the cd-index of a regular CW-sphere is itself the flag f-vector of a colored simplicial complex in a certain sense.