A subset of a permutation is said to contain if there exist such that is order isomorphic to . Here, is the symmetric group on elements.

In other words,
contains iff any *k*-subset of is order
isomorphic to .

A subset of a permutation is said to contain if there exist such that is order isomorphic to . Here, is the symmetric group on elements.

In other words,
contains iff any *k*-subset of is order
isomorphic to .

Weisstein, Eric W. "Contained Pattern."
From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/ContainedPattern.html