The Number of Inversions and the Major Index of Permutations are Asymptotically Joint-Independently Normal

Details The Number of Inversions and the Major Index of Permutations are Asymptotically Joint-Independently Normal The Number of Inversions and the Major Index of Permutations are Asymptotically Joint-Independently Normal

2010-04-07

arxiv.org/abs/1004.1160v2

Mathematics

Combinatorics

13 pages, accompanied by a Maple package <A HREF="http://www.math.rutgers.edu/~zeilberg/tokhniot/InvMaj">InvMaj</A>

Scientific paper

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.

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