Mahonian pairs

Mahonian pairs

Article history: Received 22 January 2011 Available online xxxx

Mahonian Z statistics

Mahonian STAT on words

In 2000, Babson and Steingŕımsson introduced the notion of what is now known as a permutation vincular pattern, and based on it they re-defined known Mahonian statistics and introduced new ones, proving or conjecturing their Mahonity. These conjectures were proved by Foata and Zeilberger in 2001, and by Foata and Randrianarivony in 2006. In 2010, Burstein refined some of these results by giving...

Babson-Steingŕımsson Statistics Are Indeed Mahonian (and Sometimes Even Euler-Mahonian)

Babson and Steingŕımsson have recently introduced seven new permutation statistics, that they conjectured were all Mahonian (i.e. equi-distributed with the number of inversions). We prove their conjecture for the first four, and also prove that the first and the fourth are even Euler-Mahonian. We use two different, in fact, opposite, techniques. For three of them we give a computer-generated pr...

On some Euler-Mahonian Distributions

We prove that the pair of statistics (des,maj) on multiset permutations is equidistributed with the pair (stc, inv) on certain quotients of the symmetric groups. We define an analogue of the statistic stc on multiset permutations whose joint distribution with the inversions equals that of (des,maj). We extend the definition of the statistic stc to hyperoctahedral and even hyperoctahedral groups...