2011/01/24 by Daniel Pinto, Pinto, Daniel
Mathematics · #05C10 #05C25 #20B15 #20B35 #20F05 #Advanced Topics in Algebra #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Rings, Modules, and Algebras #math.CO #math.GR #msc:05C10 #msc:05C25 #msc:20B15 #msc:20B35 #msc:20F05
paper · pdf · doi:10.48550/arxiv.1101.4621
12 pages
arxiv created 2011/01/24 · openalex publication_date 2011/01/24 · arxiv updated 2011/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Duality is the operation that interchanges hypervertices and hyperfaces on oriented hypermaps. The duality index measures how far a hypermap is from being self-dual. We say that an oriented regular hypermap has duality-type \l,n\ if l is the valency of its vertices and n is the valency of its faces. Here, we study some properties of this duality index in oriented regular hypermaps and we prove that for each pair n, l ∈ ℕ, with n,l ≥ 2, it is possible to find an oriented regular hypermap with extreme duality index and of duality-type \l,n \, even if we are restricted to hypermaps with alternating or symmetric monodromy group.