Local extrema in random permutations and the structure of longest alternating subsequences

@inproceedings{Romik2011LocalEI,
title={Local extrema in random permutations and the structure of longest alternating subsequences},
author={Dan Romik},
year={2011}
}

Let asn denote the length of a longest alternating subsequence in a uniformly random permutation of order n. Stanley studied the distribution of asn using algebraic methods, and showed in particular that E(asn) = (4n+1)/6 and Var(asn) = (32n − 13)/180. From Stanley’s result it can be shown that after rescaling, asn converges in the limit to the Gaussian distribution. In this extended abstract we present a new approach to the study of asn by relating it to the sequence of local extrema of a… CONTINUE READING