Geodesic
The Variance and the Asymptotic Distribution of the Length of Longest $k$-alternating Subsequences
Discrete mathematics & theoretical computer science, Tome 25 (2023-2024) no. 1.

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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.
DOI : 10.46298/dmtcs.10296
Classification : 05A05, 05A15, 60C05, 60F05 
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     journal = {Discrete mathematics & theoretical computer science},
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Çiçeksiz, Altar; Demirci, Yunus Emre; Işlak, Ümit. The Variance and the Asymptotic Distribution of the Length of Longest $k$-alternating Subsequences. Discrete mathematics & theoretical computer science, Tome 25 (2023-2024) no. 1. doi : 10.46298/dmtcs.10296. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.10296/

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