2003/12/04 by Margaret M. Bayer, Bayer, Margaret M.
Engineering · Mathematics · #52B05 (Primary) #52B11 #52B12 (Secondary) #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications #graph theory and CDMA systems #math.CO #msc:52B05 #msc:52B11 #msc:52B12
paper · pdf · doi:10.48550/arxiv.math/0312112
12 pages, LaTeX
arxiv created 2003/12/04 · openalex publication_date 2003/12/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Bisztriczky introduced the multiplex as a generalization of the simplex. A polytope is multiplicial if all its faces are multiplexes. In this paper it is proved that the flag vectors of multiplicial polytopes depend only on their face vectors. A special class of multiplicial polytopes, also discovered by Bisztriczky, is comprised of the ordinary polytopes. These are a natural generalization of the cyclic polytopes. The flag vectors of ordinary polytopes are determined. This is used to give a surprisingly simple formula for the h-vector of the ordinary d-polytope with n+1 vertices and characteristic k: hi=binomk-d+ii+(n-k)binomk-d+i-1i-1, for i at most d/2. In addition, a construction is given for 4-dimensional multiplicial polytopes having two-thirds of their vertices on a single facet, answering a question of Bisztriczky.