Euler–Mahonian distributions of type

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 the sense 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, along with a new proof of the generalized Carlitz identity.