A FORMULATION FOR THE GENUS SERIES FOR REGULAR MAPS

Embedding of vertex regular maps on orientable surfaces have been stud ied extensively, particularly in the case of low genus where several c lasses have proved to be tractable. However, the question of determini ng exact information about embeddings on surfaces of arbitrary genus h as proved to be less so. In this paper we show that the genus series F or vertex regular maps can be formulated elegantly as the constant ter m in a series in a way which fully captures information about the genu s. It is hoped that the cosntant term formulation will lead to further study of the genus series for regular maps. (C) 1996 Academic Press, Inc.