Stefan Felsner ; Eric Fusy ; Marc Noy - Asymptotic enumeration of orientations

dmtcs:505 - Discrete Mathematics & Theoretical Computer Science, January 1, 2010, Vol. 12 no. 2 - https://doi.org/10.46298/dmtcs.505
Asymptotic enumeration of orientationsArticle

Authors: Stefan Felsner 1; Eric Fusy 2; Marc Noy 3

  • 1 Freie Universität Berlin
  • 2 Laboratoire d'informatique de l'École polytechnique [Palaiseau]
  • 3 Departament de Matemàtica Aplicada II

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.


Volume: Vol. 12 no. 2
Published on: January 1, 2010
Imported 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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