Permutation groups arising from pattern involvement

For an arbitrary finite permutation group G , subgroup of the symmetric group S ℓ , we determine the permutations involving only members of G as ℓ -patterns, i.e. avoiding all patterns in the set S ℓ \ G . The set of all n -permutations with this property constitutes again a permutation group. We co...

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Bibliographic Details
Published inJournal of algebraic combinatorics Vol. 52; no. 3; pp. 251 - 298
Main Author Lehtonen, Erkko
Format Journal Article
LanguageEnglish
Published New York Springer US 01.11.2020
Springer Nature B.V
Subjects
Combinatorics
Computer Science
Convex and Discrete Geometry
Group theory
Group Theory and Generalizations
Lattices
Mathematics
Mathematics and Statistics
Order
Ordered Algebraic Structures
Permutations
Subgroups
Permutation pattern
Intransitive group
Imprimitive group
Galois connection
Permutation group
05A05
Primitive group
20B05
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Summary:For an arbitrary finite permutation group G , subgroup of the symmetric group S ℓ , we determine the permutations involving only members of G as ℓ -patterns, i.e. avoiding all patterns in the set S ℓ \ 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.
ISSN:0925-9899
1572-9192
DOI:10.1007/s10801-019-00902-w