Geodesic
The asymptotic number of maps on compact orientable surfaces
Diskretnaya Matematika, Tome 13 (2001) no. 2, pp. 89-98
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We get an asymptotic formula for the sum $$ Z_{N}=\sum_{b+p=N}F_{b,p}y^p, $$ where $$ F_{b,p}=\sum_{\rho=0}^\infty F_{b,p}(\rho), $$ and $F_{b,p}(\rho)$ is the number of maps of genus $\rho$ with $p+1$ vertices and $p+b$ edges. 
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     title = {The asymptotic number of maps on compact orientable surfaces},
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M. A. Krikun; V. A. Malyshev. The asymptotic number of maps on compact orientable surfaces. Diskretnaya Matematika, Tome 13 (2001) no. 2, pp. 89-98. http://geodesic.mathdoc.fr/item/DM_2001_13_2_a3/

[1] Walsh T., Lehman A., “Counting rooted maps by genus. I”, J. Comb. Theory, 13 (1972), 192–218 | DOI | MR | Zbl

[2] Wimp J., Zeilbreger D., “Resurrecting the asymptotics of linear recurrences”, J. Math. Anal. and Appl., 111 (1985), 162–176 | DOI | MR | Zbl

[3] Tutte W., “The enumerative theory of planar maps”, A Survey of Combinatorial Theory, 1973, 437–448, North Holland, Amsterdam | MR

[4] Goulden I., Jackson D., Combinatorial Enumeration, Wiley, New York, 1983 | MR | Zbl

[5] Bender E., Canfield E., Richmond L., “The asymptotic number of rooted maps on a surface. II. Enumeration by vertices and faces”, J. Comb. Theory., 63 (1993), 318–329 | DOI | MR | Zbl

[6] Edmonds J., “A combinatorial representation for polyhedral surfaces”, Notices Amer. Math. Soc., 7:646 (1960)

[7] Fernandez R., Frolich J., Sokal A., Random Walks, Critical Phenomena, and Triviality in Quantum Fields, Springer, Berlin, 1992