Canonical Representatives of Orbits of Sets

                         Steve Linton
                          St Andrews

Many search problems arising both within and outside algebra can be reduced to
finding representatives of those orbits of sets of points under a permutation
group that satisfy some condition. While clever search techniques can reduce
the number of times each orbit is encountered, it is not always possible, or
cost-effective, to reduce this number to one. It is thus necessary to reject
sets lying in previously encountered orbits, which can be done much more
efficiently if canonical representatives of the orbits can be found. This talk
will describe an algorithm (and several variations) for finding perhaps the
most obvious canonical representative: the lexicographically least set in the
orbit.