Fix-Mahonian Calculus, II: Further statistics

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:
Journal of Combinatorial Theory Series A
Year:
2008

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Abstract

Using classical transformations on the symmetric group and two transformations constructed in Fix-Mahonian Calculus I, we show that several multivariable statistics are equidistributed either with the triplet (fix,@?des,@?maj), or the pair (fix,@?maj), where ''fix,'' ''des'' and ''maj'' denote the number of fixed points, the number of descents and the major index, respectively.