%0 Journal Article
%T The Number of Inversions and the Major Index of Permutations are Asymptotically Joint-Independently Normal
%A Andrew Baxter
%A Doron Zeilberger
%J Mathematics
%D 2010
%I arXiv
%X We use recurrences (alias difference equations) to prove the longstanding conjecture that the two most important permutation statistics, namely the number of inversions and the major index, are asymptotically joint-independently-normal. We even derive more-precise-than needed asymptotic formulas for the (normalized) mixed moments. This is the fully revised second edition, incorportating the many insightful comments of nine conscientious NON-anonymous referees listed under the authors' names. This article is exclusively published in the on-line journal "Personal Journal of Shalosh B. Ekhad and Doron Zeilberger" and this arxiv.
%U http://arxiv.org/abs/1004.1160v2