Regular pseudo-oriented maps and hypermaps of low genus

Abstract

Pseudo-orientable maps were introduced by Wilson in 1976 to describe non-orientable regular maps for which it is possible to assign an orientation to each vertex in such a way that adjacent vertices have opposite orientations. This property extends naturally to non- orientable and orientable hypermaps. In this paper we classify the regular pseudo-oriented maps and hypermaps of characteristic χ > −3. With the help of GAP (The GAP group, 2014) and its library of small groups, we extend the classification down to characteristic χ = −16 (Tables 7–19 in the Appendix).