Duality on Hypermaps with Symmetric or Alternating Monodromy Group
نویسنده
چکیده
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.
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