Geodesic
Enumeration of genus-four maps by number of edges
Ars Mathematica Contemporanea, Tome 4 (2011) no. 2, pp. 351-361.

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An explicit form of the ordinary generating function for the number of rooted maps on a closed orientable surface of genus four with a given number of edges is given. An analytical formula for the number of unrooted maps of genus four with a given number of edges is obtained through the number of rooted ones. Both results are new.
DOI : 10.26493/1855-3974.132.fe2
Keywords: Enumeration, Surface, Orbifold, Rooted map, Unrooted map, Fuchsian group 
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Alexander D. Mednykh; Alain Giorgetti. Enumeration of genus-four maps by number of edges. Ars Mathematica Contemporanea, Tome 4 (2011) no. 2, pp. 351-361. doi : 10.26493/1855-3974.132.fe2. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.132.fe2/

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