Generating coset representatives for permutation groups

A group of symmetries can divide the group of all permutations of n marks into equivalence classes of isomorphs; each class is a coset of the group of symmetries. An algorithm for generating a set of isomorph, or coset, representatives is discussed. It can be used when n! is too large for all permutations to be useful, but the number of equivalence classes is manageable. The group of symmetries can be varied to match many natural notions of similarity. A computation on permutations that is restricted to a set of representatives can then concentrate on the essentially different cases.