Permutation groups arising from pattern involvement

Abstract

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

39 pages; extensively reorganized and rewritten, misprints corrected

References in corpus (1)

• Primitive permutation groups containing a cycle

Cited by in corpus (1)

• Content and singletons bring unique identification minors