The enumeration of general rooted planar maps (Q2581144)

A planar map together with a distinguished triple of mutually incident vertex, edge and face is said to be rooted. Some functional equations satisfied by the generating functions for enumerating rooted planar maps are derived. Generating functions use up to three parameters which represent the degree of the root vertex, the length of the root face, and the total number of edges of the map. In some cases the derived functional equations give rise to explicit solutions by employing the Lagrange inversion. This seems to answer a problem proposed by the second author in 1989.