Fix-Mahonian calculus, I: Two transformations

Authors:
Dominique Foata;Guo-Niu Han
Affiliations:
Institut Lothaire, 1, rue Murner, F-67000 Strasbourg, France;I.R.M.A. UMR 7501, Université Louis Pasteur et CNRS, 7, rue René-Descartes, F-67084 Strasbourg, France
Venue:
European Journal of Combinatorics
Year:
2008

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Abstract

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.