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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