EULER-MAHONIAN DISTRUBUTIONS OF TYPE Bn

Euler-Mahonian distributions of type Bn

Adin, Brenti, and Roichman introduced the pairs of statistics (ndes, nmaj) and (fdes, fmaj). They showed that these pairs are equidistributed over the hyperoctahedral group B n , and can be considered " Euler-Mahonian " in that they generalize the Carlitz identity. Further, they asked whether there exists a bijective proof of the equidistribution of their statistics. We give such a bijection, a...

Euler-mahonian Parameters on Colored Permutation Groups

New combinatorial statistics on colored permutation groups are introduced here. We present two different generalizations of major index and descent number, one of them is combinatorial in nature and the other is algebraic. We also present Euler-Mahonian type joint distributions of our parameters.

Euler-mahonian Statistics on Ordered Partitions

An ordered partition with k blocks of [n] := {1, 2, . . . , n} is a sequence of k disjoint and nonempty subsets, called blocks, whose union is [n]. Clearly the number of such ordered partitions is k!S(n, k), where S(n, k) is the Stirling number of the second kind. A statistic on ordered partitions of [n] with k blocks is called Euler-Mahonian statistics if its generating polynomial is [k]q!Sq(n...

On joint distribution of adjacencies, descents and some Mahonian statistics

We prove several conjectures of Eriksen regarding the joint distribution on permutations of the number of adjacencies (descents with consecutive values in consecutive positions), descents and some Mahonian statistics. We also prove Eriksen’s conjecture that a certain bistatistic on Viennot’s alternative tableaux is Euler-Mahonian. Résumé. Nous demontrons plusieurs conjectures d’Eriksen concerna...

Euler-Mahonian polynomials for Ca ≀ Sn