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On the length of the longest subsequence avoiding an arbitrary pattern in a random permutation

Michael H. Albert
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Abstract

We consider the distribution of the length of the longest subsequence avoiding a given pattern in a random permutation of length n. The well-studied case of a longest increasing subsequence corresponds to avoiding the pattern 21. We show that there is some constant c such that the mean value of this length is asymptotic to twice the square root of c times n and that the distribution of the length is tightly concentrated around its mean. We observe some apparent connections between c and the Stanley-Wilf limit of the class of permutations avoiding the given pattern.

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Michael H. Albert. 2005-05-31. On the length of the longest subsequence avoiding an arbitrary pattern in a random permutation. https://arxiv.org/abs/math/0505485

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