Classification of regular oriented maps and hypermaps with p (prime) (hyper)faces
Presented by Antonio BREDA D'AZEVEDO
Type: Oral presentation
Track: Maps and Symmetries
In this talk I report a join work with Maria Elisa Fernandes. In a previous paper we have classified the primer hypermaps with $p$ (prime) hyperfaces. Now we use this classification to classify the regular oriented hypermaps with a prime number of hyperfaces. The action of the (orientation preserving) automorphism group on the hyperfaces is primitive and described by a semidirect product of two cyclic groups, a cyclic group of order $p$ and the stabiliser of a hyperface. All chiral hypermaps with $p$ hyperfaces have cyclic chirality groups and those that are not canonical metacyclic have chirality index $p$. As a natural outcome we count, for each positive integer $n$ and prime $p$, the number of regular oriented hypermaps with $p$ hyperfaces of valence $n$.