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.
Cite this article
Jérémie Bouttier, Éric Fusy, Emmanuel Guitter, On the two-point function of general planar maps and hypermaps. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 1 (2014), no. 3, pp. 265–306DOI 10.4171/AIHPD/8