Geodesic
The Enumeration of Maps on the Torus and the Projective Plane
Canadian mathematical bulletin, Tome 31 (1988) no. 3, pp. 257-271

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DOI

The enumeration of rooted maps (embedded graphs), by number of edges, on the torus and projective plane, is studied. Explicit expressions for the generating functions are obtained. From these are derived asymptotic expressions and recurrence relations. Numerical tables for the numbers with up to 20 edges are presented.
DOI : 10.4153/CMB-1988-039-4
Mots-clés : 05C30, 05A15 
Bender, E. A.; Canfield, E. R. The Enumeration of Maps on the Torus and the Projective Plane. Canadian mathematical bulletin, Tome 31 (1988) no. 3, pp. 257-271. doi: 10.4153/CMB-1988-039-4
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     title = {The {Enumeration} of {Maps} on the {Torus} and the {Projective} {Plane}},
     journal = {Canadian mathematical bulletin},
     pages = {257--271},
     year = {1988},
     volume = {31},
     number = {3},
     doi = {10.4153/CMB-1988-039-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1988-039-4/}
}
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