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.

    Comment: Typos and errors corrected

    https://doi.org/10.46298/dmtcs.10296
    Source: arXiv.org:2107.12459
    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)
    Licence: Attribution-Non Commercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)

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