Geodesic
Simplification of Formulas for the Number of Maps on Surfaces
Matematičeskie zametki, Tome 83 (2008) no. 1, pp. 14-23

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Two combinatorial identities obtained by the author are used to simplify formulas for the number of general rooted cubic planar maps, for the number of $g$-essential maps on surfaces of small genus, and also for rooted Eulerian maps on the projective plane. Besides, an asymptotics for the number of maps with a large number of vertices is obtained.
Keywords: cubic planar map, $g$-essential map, surface of small genus, projective plane, Klein bottle, rooted Eulerian map, Euler beta function, gamma function, Stirling's formula. 
V. A. Voblyi. Simplification of Formulas for the Number of Maps on Surfaces. Matematičeskie zametki, Tome 83 (2008) no. 1, pp. 14-23. http://geodesic.mathdoc.fr/item/MZM_2008_83_1_a1/
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