Abstract:
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.
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