The inversion number and the major index are asymptotically jointly normally distributed on words
Combinatorics
2016-04-13 v1
Abstract
In a recent paper, Baxter and Zeilberger show 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 prove 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.
Keywords
Cite
@article{arxiv.1302.6708,
title = {The inversion number and the major index are asymptotically jointly normally distributed on words},
author = {Marko Thiel},
journal= {arXiv preprint arXiv:1302.6708},
year = {2016}
}