  We construct two bijections of the symmetric group S_n onto itself that
enable us to show that three new three-variable statistics are equidistributed
with classical statistics involving the number of fixed points. The first one
is equidistributed with the triplet (fix,des,maj), the last two with
(fix,exc,maj), where "fix," "des," "exc" and "maj" denote the number of fixed
points, the number of descents, the number of excedances and the major index,
respectively.
