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

  • Authors:

  • M. H. Albert

  • Affiliations:

  • Department of Computer Science, University of Otago, Dunedin, New Zealand

  • Venue:
  • Random Structures & Algorithms
  • Year:
  • 2007

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Abstract

We consider the distribution of the length of the longestsubsequence avoiding an arbitrary pattern, π, in a randompermutation of length n. The well-studied case of a longestincreasing subsequence corresponds to π = 21. We show that thereis some constant cπ such that as n➝ ∞ the mean value of this length is asymptotic to√cπn and that the distribution of the length istightly concentrated around its mean. We observe some apparentconnections between cπ and the StanleyWilflimit of the class of permutations avoiding the pattern À.© 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2007