A Formulation for the Genus Series for Regular Maps

Embedding of vertex regular maps on orientable surfaces have been studied extensively, particularly in the case of low genus where several classes have proved to be tractable. However, the question of determining exact information about embeddings on surfaces of arbitrary genus has proved to be less so. In this paper we show that the genus series for vertex regular maps can be formulated elegantly as the constant term in a series in a way which fully captures information about the genus. It is hoped that the cosntant term formulation will lead to further study of the genus series for regular maps.