Authors: Marie Albenque ¹; Jérémie Bouttier ^2,3

• 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.