an:06244222
Zbl 1301.05179
Walsh, Timothy R.
Counting maps on doughnuts
EN
Theor. Comput. Sci. 502, 4-15 (2013).
00328231
2013
j
05C30
rooted maps; unrooted maps; orientable surfaces; exact enumeration; generating functions; orbifolds
Summary: How many maps with \(V\) vertices and \(E\) edges can be drawn on a doughnut with \(G\) holes? I solved this problem for doughnuts with up to 10 holes, and my colleagues \textit{A. Giorgetti} and \textit{A. Mednykh} [Ars Math. Contemp. 4, No. 2, 351--361 (2011; Zbl 1237.05104)] counted maps by number of edges alone on doughnuts with up to 11 holes. This expository paper outlines, in terms meant to be understandable by a non-specialist, the methods we used and those used by other researchers to obtain the results upon which our own research depends.
Zbl 1237.05104