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Discrete Mathematics & Theoretical Computer Science |
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.10296The Variance and the Asymptotic Distribution of the Length of Longest
$k$-alternating SubsequencesArticle
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.
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)
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