##### submitted for publication

# Dominique Foata, Guo-Niu Han

#
FIX-MAHONIAN CALCULUS, I: TWO TRANSFORMATIONS

**Abstract.**
We construct two bijections of the symmetric group
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.

foata at math dot u-strasbg dot fr,
guoniu at math dot u-strasbg dot fr

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