SIAM Journal on Discrete Mathematics
The permutation π of length n, written in one-line notation as π (1)π (2)· · · π (n), is said to contain the permutation σ if π has a subsequence that is order isomorphic to σ, and each such subsequence is said to be an occurrence of σ in π or simply a σ pattern. For example, π = 491867532 contains σ = 51342 because of the subsequence π (2)π (3)π (5)π (6)π (9) = 91672. Permutation containment is easily seen to be a partial order on the set of all (finite) permutations, which we simply denote by ≤. If the permutation π fails to contain σ we say that π avoids σ.
Brignall, Robert; Ekhad, Shalosh B.; Smith, Rebecca; and Vatter, Vincent, "Almost Avoiding Permutations" (2009). Open Dartmouth: Faculty Open Access Scholarship. 2530.