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

Jérémie Bouttier, Éric Fusy, Emmanuel Guitter
2014 Annales de l'Institut Henri Poincaré D  
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
more » ... ir number of dark faces, and finally general and bipartite maps counted by both their number of edges and their number of faces.
doi:10.4171/aihpd/8 fatcat:arba3zmz4vbrjgbts2yushi5wa