Computational Algebra Seminar: Evans -- Orderly generation of generating sets

Speaker: Rhys Evans (Magma, Sydney)
Title: Orderly generation of generating sets
Time & Place: 15:00-16:00, Thursday 26 March, SMRI Seminar Room 
Abstract: 
In general, the enumeration of discrete objects is computationally hard.  
However, for many highly symmetrical discrete objects, their description as a finite 
group together with a generating set with certain properties often allows for more 
efficient computation and deeper theory (e.g., regular maps, maniplexes and 
Cayley graphs).

In this talk, we will see the application of an orderly generation algorithm to the
enumeration of minimal generating sets of a given group.  Simple group-theoretical
observations will be used to improve on a basic algorithm, extending previous
enumerations to groups of much larger order.  This has been used to generate a complete
list of minimal Cayley graphs on up to 511 vertices.  I will also mention other
collections of highly symmetrical discrete objects, and the databases and packages that
make the resulting collections of objects available to a wider audience.  

This is based on joint work with Primoz Potocnik and Kolja Knauer.