A Note on the Stanley Distribution
Shalosh B. Ekhad
TL;DR
This paper refines the asymptotic analysis of the moments of the largest up-down subsequence length in random permutations, building on Stanley's proof of asymptotic normality.
Contribution
It provides a more precise asymptotic formula for the moments of the distribution, extending Stanley's original results.
Findings
Derived a refined asymptotic formula for moments
Confirmed asymptotic normality of the distribution
Enhanced understanding of the distribution's behavior
Abstract
Richard Stanley proved that the centralized/normalized version of the random variable "length of largest up-down subsequence" in a random permutation of length n is asymptotically normal. We go beyond and present a more refined asymptotic formula for the moments.
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Taxonomy
TopicsBayesian Methods and Mixture Models · Statistical Distribution Estimation and Applications · Stochastic processes and statistical mechanics