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

Recep 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 t…