Using large random permutations to partition permutation classes
Pure Mathematics and Applications, Volume 30 (2022), Issue 1, Pages 31–36
Christian, Émile, Jay and Henning
Permutation classes are sets of permutations defined by the absence of certain substructures. In some cases permutation classes can be decomposed as unions of subclasses. We use combinatorial specifications automatically discovered by Combinatorial Exploration (Albert et al. 2022) to uniformly generate large random permutations in a permutation class, and apply clustering methods to partition them into interesting subclasses. We seek to automate as much of this process as possible.