Minimal and canonical images
Christopher Jefferson, Eliza Jonauskyte, Markus Pfeiffer, Rebecca Waldecker · Journal of Algebra · 2018
We describe a family of new algorithms for finding the canonical image of a set of points under the action of a permutation group. This family of algorithms makes use of the orbit structure of the group, and a chain of subgroups of the group, to efficiently reduce the amount of search that must be performed to find a canonical image. We present a formal proof of correctness of our algorithms and describe experiments on different permutation groups that compare our algorithms with the previous state of the art.