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Enumeration of genus-four maps by number of edges. (English) Zbl 1237.05104
Summary: 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.

MSC:
05C30 Enumeration in graph theory
57R18 Topology and geometry of orbifolds
20H10 Fuchsian groups and their generalizations (group-theoretic aspects)
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