Some unexpected consequences of symmetry computations

Abstract

This paper gives some instances of experimental computations involving the action of groups on graphs and maps with a high degree of symmetry, that have led to unexpected theoretical discoveries. These include new presentations for 3-dimensional special linear groups, a closed-form definition for the binary reflected Gray codes, a new theorem on groups expressible as a product of an abelian group and a cyclic group, and some revealing observations about the genus spectrum of particular classes of regular maps on surfaces.