Altar Çiçeksiz ; Yunus Emre Demirci ; Ümit Işlak - The Variance and the Asymptotic Distribution of the Length of Longest $k$-alternating Subsequences

dmtcs:10296 - Discrete Mathematics & Theoretical Computer Science, May 5, 2023, vol. 25:1 - https://doi.org/10.46298/dmtcs.10296
The Variance and the Asymptotic Distribution of the Length of Longest $k$-alternating SubsequencesArticle

Authors: Altar Çiçeksiz ; Yunus Emre Demirci ; Ümit Işlak

    We obtain an explicit formula for the variance of the number of $k$-peaks in a uniformly random permutation. This is then used to obtain an asymptotic formula for the variance of the length of longest $k$-alternating subsequence in random permutations. Also a central limit is proved for the latter statistic.


    Volume: vol. 25:1
    Section: Combinatorics
    Published on: May 5, 2023
    Accepted on: March 12, 2023
    Submitted on: November 12, 2022
    Keywords: Mathematics - Probability,Mathematics - Combinatorics,05A05 (Primary), 60F05 (Secondary)

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