Journal of Integer Sequences, Vol. 22 (2019), Article 19.5.1

A Note on a Permutation Statistic

Tamás Lengyel
Occidental College
1600 Campus Road
Los Angeles, CA 90041


We study the length of the initial up-down alternating segment of a permutation of [n] selected uniformly at random. It turns out that as n tends to infinity, the expected value and the standard deviation of this statistic converge to small constants.

Full version:  pdf,    dvi,    ps,    latex    

(Concerned with sequence A000111.)

Received July 28 2019; revised versions received August 16 2019; August 19 2019. Published in Journal of Integer Sequences, August 19 2019.

Return to Journal of Integer Sequences home page