Abstract
Adin, Brenti, and Roichman [R.M. Adin, F. Brenti, Y. Roichman, Descent numbers and major indices for the hyperoctahedral group, Adv. in Appl. Math. 27 (2001) 210–224], in answering a question posed by Foata, introduced two descent numbers and major indices for the hyperoctahedral group
B
n
, whose joint distribution generalizes an identity due to MacMahon and Carlitz. We shall show that yet another pair of statistics exists, and whose joint distribution constitutes a “natural” solution to Foata's problem.