A classification of mahonian maj-inv statistics

A Classification of Mahonian Maj-inv Statistics

Two well known mahonian statistics on words are the inversion number and the major index. In 1996, Foata and Zeilberger introduced generalizations, parameterized by relations, of these statistics. In this paper, we study the statistics which can be written as a sum of these generalized statistics. This leads to generalizations of some classical results. In particular, we characterize all such r...

A maj-inv BIJECTION FOR C2 ≀ An

We give a bijective proof of the MacMahon-type equidistribution over the group of signed even permutations C2 ≀ An that was stated in [Bernstein. Electron. J. Combin. 11 (2004) 83]. This is done by generalizing the bijection that was introduced in the bijective proof of the equidistribution over the alternating group An in [Bernstein and Regev. Sém. Lothar. Combin. 53 (2005) B53b].

Simultaneous Maj Statistics

The generating function for words with several simultaneous maj weights is given. New maj-like Mahonian statistics result. Some applications to integer partitions are given.

Mahonian Z statistics

An Eulerian Partner for Inversions

A number of researchers studying permutation statistics on the symmetric group Sn have considered pairs (x, Y), where x is an Eulerian statistic and Y is a Mahonian statistic. Of special interest are pairs such as (des, maj), whose joint distribution on Sn is given by Carlitz’s q-Eulerian polynomials. We present a natural Eulerian statistic stc such that the pair (stc, inv) is equally distribut...