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The distribution of increasing l-sequences in random permutations: a Markov chain approach

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  • Johnson, Brad C.
  • Fu, James C.

Abstract

This paper examines the distribution of increasing l-sequences in a random permutation generated by the integers 1,...,n; an increasing l-sequence being a sequence of l consecutive integers. The exact distribution is obtained by a finite Markov chain embedding technique in combination with a conditioning argument. The result is easy to implement, intuitively simple and can be generalized.

Suggested Citation

  • Johnson, Brad C. & Fu, James C., 2000. "The distribution of increasing l-sequences in random permutations: a Markov chain approach," Statistics & Probability Letters, Elsevier, vol. 49(4), pages 337-344, October.
    • Handle: RePEc:eee:stapro:v:49:y:2000:i:4:p:337-344
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    References listed on IDEAS

    as
    1. James Fu, 1995. "Exact and limiting distributions of the number of successions in a random permutation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(3), pages 435-446, September.
    2. Fu, James C. & Lou, W. Y. Wendy & Wang, Yueh-Jir, 1999. "On the exact distributions of Eulerian and Simon Newcomb numbers associated with random permutations," Statistics & Probability Letters, Elsevier, vol. 42(2), pages 115-125, April.
    3. M. Koutras & V. Alexandrou, 1995. "Runs, scans and URN model distributions: A unified Markov chain approach," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(4), pages 743-766, December.
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    Cited by:

    1. James C. Fu, 2012. "On the Distribution of the Number of Occurrences of an Order-Preserving Pattern of Length Three in a Random Permutation," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 831-842, September.
    2. Tung-Lung Wu, 2013. "On Finite Markov Chain Imbedding and Its Applications," Methodology and Computing in Applied Probability, Springer, vol. 15(2), pages 453-465, June.
    3. Johnson, Brad C., 2002. "The distribution of increasing 2-sequences in random permutations of arbitrary multi-sets," Statistics & Probability Letters, Elsevier, vol. 59(1), pages 67-74, August.

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