2011/01/25 by Daniel Pinto, Pinto, Daniel
Decision Sciences · Mathematics · #05C10 #05C25 #20F05 #Advanced Topics in Algebra #Combinatorics (math.CO) #FOS: Mathematics #Fuzzy and Soft Set Theory #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1101.4814
openalex publication_date 2011/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
By adapting the notion of chirality group, the duality group of \cal H can be defined as the the minimal subgroup D(\cal H) \trianglelefteq Mon(\cal H) such that \cal H/D(\cal H) is a self-dual hypermap (a hypermap isomorphic to its dual). Here, we prove that for any positive integer d, we can find a hypermap of that duality index (the order of D(\cal H)), even when some restrictions apply, and also that, for any positive integer k, we can find a non self-dual hypermap such that |Mon(\cal H)|/d=k. This k will be called the duality coindex of the hypermap.