Marie Albenque ; Jérémie Bouttier - Constellations and multicontinued fractions: application to Eulerian triangulations

dmtcs:3084 - Discrete Mathematics & Theoretical Computer Science, January 1, 2012, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) - https://doi.org/10.46298/dmtcs.3084
Constellations and multicontinued fractions: application to Eulerian triangulationsArticle

Authors: Marie Albenque 1; Jérémie Bouttier ORCID2,3

  • 1 Laboratoire d'informatique de l'École polytechnique [Palaiseau]
  • 2 Institut de Physique Théorique - UMR CNRS 3681
  • 3 Laboratoire d'informatique Algorithmique : Fondements et Applications

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.


Volume: DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
Section: Proceedings
Published on: January 1, 2012
Imported on: January 31, 2017
Keywords: planar maps, Eulerian triangulations, continued fractions, lattice paths,Constellations,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
Funding:
    Source : OpenAIRE Graph
  • Combinatorial methods, from enumerative topology to random discrete structures and compact data representations.; Funder: European Commission; Code: 208471; Call ID: ERC-2007-StG; Projet Financing: EC:FP7:ERC

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