Constellations and multicontinued fractions: application to Eulerian triangulations

Details Constellations and multicontinued fractions: application to Eulerian triangulations Constellations and multicontinued fractions: application to Eulerian triangulations

2011-12-29

arxiv.org/abs/1112.6379v1

Mathematics

Combinatorics

12 pages, 4 figures

Scientific paper

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.

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