Permutation groups arising from pattern involvement

DOI10.1007/S10801-019-00902-WarXiv1605.05571WikidataQ127196219 ScholiaQ127196219MaRDI QIDQ6273651

Erkko Lehtonen

Publication date: 18 May 2016

Abstract: For an arbitrary finite permutation group $G$, subgroup of the symmetric group $S_{e}ll$, we determine the permutations involving only members of $G$ as $ell$-patterns, i.e., avoiding all patterns in the set $S_{e}llsetminusG$. 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.

Mathematics Subject Classification ID

Permutations, words, matrices (05A05) General theory for finite permutation groups (20B05)

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