Counting unrooted hypermaps on closed orientable surface
نویسندگان
چکیده
In this paper we derive an enumeration formula for the number of hypermaps of given genus g and given number of darts n in terms of the numbers of rooted hypermaps of genus γ ≤ g with m darts , where m|n. Résumé. Dans ce travail on denombre les hypergraphes d’un genus g donné, et un nombr e de fleches n, selon le nombre de hyper cartes de genus γ ≤ g, et av ec m fleches, ou m|n.
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Enumeration of unrooted hypermaps of a given genus
In this paper we derive an enumeration formula for the number of hypermaps of a given genus g and given number of darts n in terms of the numbers of rooted hypermaps of genus γ ≤ g with m darts, where m|n. Explicit expressions for the number of rooted hypermaps of genus g with n darts were derived by Walsh (1975) for g = 0, and by Arques (1987) for g = 1. We apply our general counting formula t...
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