Counting maps on doughnuts

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 Alain Giorgetti and Alexander Mednykh counted maps by number of edges alone on doughnuts with up to 11 holes. This expository paper outlines,...

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Bibliographic Details
Published in:Theoretical computer science Vol. 502; pp. 4 - 15
Main Author: Walsh, Timothy R.
Format: Journal Article
Language:English
Published: Elsevier B.V 02.09.2013
Subjects:
Exact enumeration
Generating functions
Orbifolds
Orientable surfaces
Rooted maps
Unrooted maps
Orientable surfaces
Exact enumeration
Rooted maps
Orbifolds
Unrooted maps
Generating functions
ISSN:0304-3975, 1879-2294
Online Access:Get full text
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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 Alain Giorgetti and Alexander Mednykh 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.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2011.08.026