Babson–Steingrı́msson Statistics are Indeed Mahonian (and Sometimes Even Euler–Mahonian)

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...

Mahonian Z statistics

Graphical Mahonian Statistics on Words

Foata and Zeilberger defined the graphical major index, majU , and the graphical inversion index, invU , for words over the alphabet {1, 2, . . . , n}. These statistics are a generalization of the classical permutation statistics maj and inv indexed by directed graphs U . They showed that majU and invU are equidistributed over all rearrangement classes if and only if U is bipartitional. In this...

Statistics on staircase tableaux, eulerian and mahonian statistics

We give a simple bijection between some staircase tableaux and tables of inversion. Some nice properties of the bijection allows us to define some q-Eulerian polynomials related to the staircase tableaux. We also give a combinatorial interpretation of these q-Eulerian polynomials in terms of permutations. Résumé. Nous proposons une bijection simple entre certains tableaux escalier et les tables...

Fix-euler-mahonian Statistics on Wreath Products

In 1997 Clarke, Han, and Zeng introduced a q-analogue of Euler’s difference table for n! using a key bijection Ψ on symmetric groups. In this paper we extend their results to the wreath product of a cyclic group with the symmetric group. By generalizing their bijection Ψ we prove the equidistribution of the triple statistics (fix, exc, fmaj) and (fix, exc, fmaf) on wreath products, where “fix”,...