Hypermaps versus bipartite maps

Abstract A hypermap was defined by R. Cori to be a pair of permutations σ and α on a finite set B , such that the group generated by σ and α is transitive on B . The genus of a hypermap was defined according to a formula of A. Jacques for the genus of a pair of permutations. This paper presents a one-to-one correspondence between the set of hypermaps of a given genus and the set of 2-colored bipartite maps of the same genus.