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On the Distribution of the Length of the Longest Increasing Subsequence in a Random Permutation

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  • James C. Fu

    (University of Manitoba)

  • Yu-Fei Hsieh

    (University of Manitoba)

Abstract

The distribution of the longest increasing subsequence in a random permutation has attracted many researchers in statistics, computer sciences and mathematics. There are considerable manuscripts studying the distribution especially for large n. In this short manuscript, we provide a simple probabilistic approach to obtain the exact distribution of the length of the longest increasing subsequence of a random permutation, based on the insertion procedure and the finite Markov chain imbedding technique.

Suggested Citation

  • James C. Fu & Yu-Fei Hsieh, 2015. "On the Distribution of the Length of the Longest Increasing Subsequence in a Random Permutation," Methodology and Computing in Applied Probability, Springer, vol. 17(2), pages 489-496, June.
    • Handle: RePEc:spr:metcap:v:17:y:2015:i:2:d:10.1007_s11009-013-9376-1
    DOI: 10.1007/s11009-013-9376-1
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    References listed on IDEAS

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    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. 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.
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    Cited by:

    1. Yin, Juan & Cui, Lirong & Balakrishnan, Narayanaswamy, 2022. "Reliability of consecutive-(k,l)-out-of-n: F systems with shared components under non-homogeneous Markov dependence," Reliability Engineering and System Safety, Elsevier, vol. 224(C).
    2. Ayat Al-Meanazel & Brad C. Johnson, 2020. "The Distribution of the Length of the Longest Increasing Subsequence in Random Permutations of Arbitrary Multi-sets," Methodology and Computing in Applied Probability, Springer, vol. 22(3), pages 1009-1021, September.

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