Duality on hypermaps with symmetric or alternating monodromy group

Daniel Pinto
2012 Ars Mathematica Contemporanea  
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
more » ... ular hypermap with extreme duality index and of duality-type {l, n}, even if we are restricted to hypermaps with alternating or symmetric monodromy group.
doi:10.26493/1855-3974.206.a03 fatcat:67wd6kgifzh6xf7z7k4i64b4vy