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The Inversion Number and the Major Index are Asymptotically Jointly Normally Distributed on Words

Part of: Combinatorics

Published online by Cambridge University Press:  14 January 2016

MARKO THIEL
MARKO THIEL*
Affiliation:
Institut für Mathematik, Universität Zürich (e-mail: markth@math.uzh.ch)
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Abstract

In a recent paper, Baxter and Zeilberger showed that the two most important Mahonian statistics, the inversion number and the major index, are asymptotically independently normally distributed on permutations. In another recent paper, Canfield, Janson and Zeilberger proved the result, already known to statisticians, that the Mahonian distribution is asymptotically normal on words. This leaves one question unanswered: What, asymptotically, is the joint distribution of the inversion number and the major index on words? We answer this question by establishing convergence to a bivariate normal distribution.

MSC classification

Primary: 05A05: Permutations, words, matrices
Secondary: 05A16: Asymptotic enumeration
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 25 , Issue 3 , May 2016 , pp. 470 - 483
Copyright
Copyright © Cambridge University Press 2016 

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References

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