This paper describes the determination of all orientably-regular maps and hypermaps of
genus 2 to 101, and all non-orientable regular maps and hypermaps of genus 3 to 202. It …

An orientably-regular map $ M $ is a 2-cell embedding of a connected graph in a closed,
orientable surface, with the property that the group $\mathrm {Aut}^\textrm {o} M $ of all …

We formulate conditions on a set of log-concave sequences, under which any linear
combination of those sequences is log-concave, and further, of conditions under which …

An abstract polytope of rank is said to be chiral if its automorphism group has precisely two
orbits on the flags, such that adjacent flags belong to distinct orbits. This paper describes a …

Developments and open problems on chiral polytopes Page 1 Also available at http://amc.imfm.si
ISSN 1855-3966 (printed edn.), ISSN 1855-3974 (electronic edn.) ARS MATHEMATICA …

Dessins d'enfants can be regarded as bipartite graphs embedded in compact orientable
surfaces. According to Grothendieck and others, a dessin uniquely determines a complex …

We classify compact Riemann surfaces of genus $ g $, where $ g-1$ is a prime $ p $, which
have a group of automorphisms of order $\rho (g-1) $ for some integer $\rho\ge 1$, and …

The automorphism group of every abstract regular polytope of type {k1|⋯| km} is a smooth
finite quotient of the corresponding Coxeter group [k1,…, km] satisfying a particular condition …

We prove the existence of infinitely many orientably-regular but chiral maps of every given
hyperbolic type, by constructing base examples from suitable permutation representations of …

Bi-orientable maps (also called pseudo-orientable maps) were introduced by Wilson in the
1970s to describe non-orientable maps with the property that opposite orientations can …