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Matematicheskie Zametki, 2008, Volume 83, Issue 1, Pages 14–23
DOI: https://doi.org/10.4213/mzm3766 (Mi mzm3766) 		 
Simplification of Formulas for the Number of Maps on Surfaces

V. A. Voblyi

N. E. Bauman Moscow State Technical University
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DOI: https://doi.org/10.4213/mzm3766
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.
Received: 25.12.2006
Revised: 13.06.2007
English version:
Mathematical Notes, 2008, Volume 83, Issue 1, Pages 14–22
DOI: https://doi.org/10.1134/S0001434608010021
Bibliographic databases:
UDC: 519.175.3
Language: Russian
Citation: V. A. Voblyi, “Simplification of Formulas for the Number of Maps on Surfaces”, Mat. Zametki, 83:1 (2008), 14–23; Math. Notes, 83:1 (2008), 14–22
Citation in format AMSBIB
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