We find the asymptotic number of 2-orientations of quadrangulations with n inner faces, and of 3-orientations of triangulations with n inner vertices. We also find the asymptotic number of prime 2-orientations (no separating quadrangle) and prime 3-orientations (no separating triangle). The estimates we find are of the form c . n(-alpha)gamma(n), for suitable constants c, alpha, gamma with alpha = 4 for 2-orientations and alpha = 5 for 3-orientations. The proofs are based on singularity analysis of D-finite generating functions, using the Fuchsian theory of complex linear differential equations.

Source : oai:HAL:hal-00990467v1

Volume: Vol. 12 no. 2

Published on: January 1, 2010

Submitted on: March 26, 2015

Keywords: Orientation,Quadrangulation,Triangulation,D-finite generating function,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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