2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60570We introduce and study three new statistics on the hyperoctahedral group $B_{n}$, and show that they give two generalizations of Carlitz's identity for the descent number and major index over $S_{n}$. This answers a question posed by Foata.16 pagesCombinatoricstext