Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. n combinatorial mathematics and theoretical computer science, a permutation pattern is a sub-permutation of a longer permutation. The permutation π written in the one-line notation is said to contain the permutation σ if there exists a subsequence of entries of π that has the same relative order as σ, and in this case σ is said to be a pattern of π, written σ ≤ π. Otherwise, π is said to avoid the permutation σ. The subsequence of π need not consist of consecutive entries. For example, permutation π = 391867452 (written in one-line notation) contains the pattern σ = 51342, as can be seen by considering the subsequence 91672. Such a subsequence is called a copy of σ.