  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.
