Geodesic
Constellations and multicontinued fractions: application to Eulerian triangulations
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012), DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) (2012).

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We consider the problem of enumerating planar constellations with two points at a prescribed distance. Our approach relies on a combinatorial correspondence between this family of constellations and the simpler family of rooted constellations, which we may formulate algebraically in terms of multicontinued fractions and generalized Hankel determinants. As an application, we provide a combinatorial derivation of the generating function of Eulerian triangulations with two points at a prescribed distance. 
@article{DMTCS_2012_special_263_a70,
     author = {Albenque, Marie and Bouttier, J\'er\'emie},
     title = {Constellations and multicontinued fractions: application to {Eulerian} triangulations},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)},
     year = {2012},
     doi = {10.46298/dmtcs.3084},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3084/}
}
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%A Bouttier, Jérémie
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%J Discrete mathematics & theoretical computer science
%D 2012
%V DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
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Albenque, Marie; Bouttier, Jérémie. Constellations and multicontinued fractions: application to Eulerian triangulations. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012), DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) (2012). doi : 10.46298/dmtcs.3084. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3084/

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