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

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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.

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Authors and Affiliations

  1. Department of Statistics, University of Manitoba, Winnipeg, MB, Canada, R3T 2N2

    James C. Fu & Yu-Fei Hsieh

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  1. James C. Fu
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  2. Yu-Fei Hsieh
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Correspondence to Yu-Fei Hsieh.

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Fu, J.C., Hsieh, YF. On the Distribution of the Length of the Longest Increasing Subsequence in a Random Permutation. Methodol Comput Appl Probab 17, 489–496 (2015). https://doi.org/10.1007/s11009-013-9376-1

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  • DOI: https://doi.org/10.1007/s11009-013-9376-1

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