Permutation groups arising from pattern involvement

Journal of Algebraic Combinatorics, 52 (2020), 251–298
http://doi.org/10.1007/s10801-019-00902-w

For an arbitrary finite permutation group G, subgroup of the symmetric group Sl, we determine the permutations involving only members of G as l-patterns, i.e. avoiding all patterns in the set Sl\G. The set of all n-permutations with this property constitutes again a permutation group. We consequently refine and strengthen the classification of sets of permutations closed under pattern involvement and composition that is due to Atkinson and Beals.