Latin squares with specified autotopisms

From this page you can download Latin squares of orders up to 17 that have any specified autotopism (at least, you can specify the cycle structure of the autotopism, from this it is easy to get any autotopism you might want). These squares were constructed by my former PhD student Doug Stones using gap code which can be downloaded here. That code can be used to create larger examples with specified autotopisms.

This work was performed for our paper:

D. S. Stones, P. Vojtechovský and I. M. Wanless, Cycle structure of autotopisms of quasigroups and Latin squares.

There are also some specific larger examples displaying interesting behaviour.

These three examples answer a question about autotopisms of Latin squares of prime order, asked in the paper of Stones et al. [above]. Another question from that paper is answered by the following examples of quasigroups possessing an automorphism of order more than the order of the quasigroup.

While you are here you might also be interested in

  • the equivalent page for autoparatopisms
  • Latin squares with transitive autotopism groups

    Back to Latin squares data homepage.