Mahonian statistics on labeled forests (Q1191953)

A permutation statistic having the same distribution on the symmetric group \(S_ n\) as the inversion statistic is called Mahonian statistic, and inversion index and major index are the fundamental examples of Mahonian statistics. In this paper the authors, by using a bijection on labeled forests, prove that the major index has the same distribution as the inversion index on labeled forests. In addition some new results dealing with more general statistics on labeled forests are obtained by a generalized version of the bijection introduced here.