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

Altar Çiçeksiz , Yunus Emre Demirci, Ümit Işlak

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

Altar Çiçeksiz , Yunus Emre Demirci, Ümit Işlak

Abstract

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

Keywords

• Mathematics - Probability
• Mathematics - Combinatorics
• 05A05 (Primary), 60F05 (Secondary)

Mathematics Subject Classification 2020

• 05A05 - Permutations, words, matrices
• 05A15 - Exact enumeration problems, generating functions
• 60C05 - Combinatorial probability
• 60F05 - Central limit and other weak theorems

Linked publications - datasets - software

• Has review

  Review available on zbMATH Open, by Nikolaos Fountoulakis (Birmingham) (English)

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