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Contained Pattern

A pattern alpha in S_k is contained in tau in S_n if there exist 1<=i_1<...<i_k<=n such that tau=(tau_i,...,tau_k) is order isomorphic to alpha=(alpha_1,...,alpha_k). Here, S_n is the symmetric group on the n-element set {1,...,n}.

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

See also

Avoided Pattern, Order Isomorphic, Permutation Pattern, Wilf Class, Wilf Equivalent

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References

Mansour, T. "Permutations Avoiding a Pattern from S_k and at Least Two Patterns from S_3." 31 Jul 2000. https://arxiv.org/abs/math/0007194.

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Contained Pattern

Cite this as:

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

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