On the two-point function of general planar maps and hypermaps

Jérémie Bouttier (1, 2) , Éric Fusy (3) , Emmanuel Guitter (2)

1 DMA - Département de Mathématiques et Applications - ENS Paris
2 IPHT - Institut de Physique Théorique - UMR CNRS 3681
3 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]

We consider the problem of computing the distance-dependent two-point function of general planar maps and hypermaps, i.e. the problem of counting such maps with two marked points at a prescribed distance. The maps considered here may have faces of arbitrarily large degree, which requires new bijections to be tackled. We obtain exact expressions for the following cases: general and bipartite maps counted by their number of edges, 3-hypermaps and 3-constellations counted by their number of dark faces, and finally general and bipartite maps counted by both their number of edges and their number of faces.

Domaines: Combinatoire [math.CO]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Jérémie Bouttier, Éric Fusy, Emmanuel Guitter. On the two-point function of general planar maps and hypermaps. Annales de l'Institut Henri Poincaré, 2014, 1 (3), ⟨10.4171/AIHPD/8⟩. ⟨hal-00914145⟩