Enumeration of simple bipartite maps on the sphere and the projective plane Original Research Article

This paper is concerned with the number of rooted simple bipartite maps on the plane according to the root-face valencies and the number of edges of the maps. An explicit formula with one parameter is given. Furthermore, a special kind of rooted simple bipartite maps on the projective plane are counted and, as special cases, recursive formulae for maps with fewer faces on the projective plane are presented as well.