Minimal and canonical images

Christopher Jefferson, Eliza Jonauskyte, Markus Pfeiffer, Rebecca Waldecker

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)
3 Downloads (Pure)


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.
Original languageEnglish
Pages (from-to)481-506
JournalJournal of Algebra
Early online date22 Nov 2018
Publication statusPublished - 1 Mar 2019


  • Minimal images
  • Canonical images
  • Computation
  • Group theory
  • Permutation groups


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