The Variance and the Asymptotic Distribution of the Length of Longest $k$-alternating Subsequences

Autor: Altar Çiçeksiz, Yunus Emre Demirci, Ümit Işlak
Jazyk: angličtina
Rok vydání: 2023
Předmět:
Zdroj: Discrete Mathematics & Theoretical Computer Science, Vol vol. 25:1, Iss Combinatorics (2023)
Druh dokumentu: article
ISSN: 1365-8050
DOI: 10.46298/dmtcs.10296
Popis: 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.
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