Geodesic
Duality on hypermaps with symmetric or alternating monodromy group
Ars Mathematica Contemporanea, Tome 5 (2012) no. 2, pp. 259-267.

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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 the duality index of oriented regular hypermaps and we prove that for each pair n, l ∈ N, with n, l ≥ 2 (but not both equal to 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.
DOI : 10.26493/1855-3974.206.a03
Keywords: hypermaps, duality, primitive groups, alternating group, symmetric group, generators 
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Daniel Pinto. Duality on hypermaps with symmetric or alternating monodromy group. Ars Mathematica Contemporanea, Tome 5 (2012) no. 2, pp. 259-267. doi : 10.26493/1855-3974.206.a03. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.206.a03/

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