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

Mednykh, Alexander; Giorgetti, Alain

Ars Math. Contemp. 4, No. 2, 351-361 (2011).

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)

Keywords:

generating function; number of rooted maps; closed orientable surface; genus four; unrooted maps