Singular maps on the Klein bottle (Q1847636)

A map on a surface is called singular if it has only one face. This paper presents a two-parameter generating function for counting rooted singular maps on the Klein bottle by the number of edges and the valency of the root-vertex and an explicit formula for counting these maps by the number of edges alone. The paper then includes the set of vertex valencies as a parameter and presents a functional equation satisfied by the corresponding generating function.