Permutation groups arising from pattern involvement

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For an arbitrary finite permutation group G, subgroup of the symmetric group S, we determine the permutations involving only members of G as ℓ-patterns, i.e. avoiding all patterns in the set S\ 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.

Original languageBritish English
Pages (from-to)251-298
Number of pages48
JournalJournal of Algebraic Combinatorics
Issue number3
StatePublished - 1 Nov 2020


  • Galois connection
  • Imprimitive group
  • Intransitive group
  • Permutation group
  • Permutation pattern
  • Primitive group


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