In this paper we compute the chirality group, the chirality index and the smallest regular coverings of the chiral toroidal maps. We also compute the greatest regular maps covered by chiral toroidal… (More)

We use the conceptual idea of “maps on orbifolds” and the theory of the nonEuclidian crystallographic groups (NEC groups) to enumerate rooted and unrooted maps (both sensed and unsensed) on surfaces… (More)

A hypermap is (hypervertex-) bipartite if its hypervertices can be 2-coloured in such a way that “neighbouring” hypervertices have different colours. It is bipartiteuniform if within each of the sets… (More)

The central question of this paper is the Genus Question: For which N is it possible to draw a regular map or hypermap on the non-orientable surface of characteristic −N? We answer this question for… (More)

In the present paper we introduce a family of functors (called operations) of the category of hypermaps (dessins) preserving the underlying Riemann surface. The considered family of functors include… (More)

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… (More)