Geodesic
Asymptotic enumeration of orientations
Discrete mathematics & theoretical computer science, Tome 12 (2010) no. 2.

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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. 
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     author = {Felsner, Stefan and Fusy, Eric and Noy, Marc},
     title = {Asymptotic enumeration of orientations},
     journal = {Discrete mathematics & theoretical computer science},
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     number = {2},
     year = {2010},
     doi = {10.46298/dmtcs.505},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.505/}
}
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Felsner, Stefan; Fusy, Eric; Noy, Marc. Asymptotic enumeration of orientations. Discrete mathematics & theoretical computer science, Tome 12 (2010) no. 2. doi : 10.46298/dmtcs.505. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.505/

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