Enumeration of genus-four maps by number of edges

Alexander D. Mednykh, Alain Giorgetti

Abstract


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.


Keywords


Enumeration, Surface, Orbifold, Rooted map, Unrooted map, Fuchsian group

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DOI: https://doi.org/10.26493/1855-3974.132.fe2

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications