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Permutation groups arising from pattern involvement

Lehtonen, Erkko

Journal of Algebraic Combinatorics, 52 (2020), 251–298

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.