Math. Nachrichten, 83 (1978), p.143-159.

Dominique Foata and M.-P. Schütenberger

Major Index and Inversion Number of Permutations

Abstract. Two bijections F and G of the symmetric group S_n on itself are constructed that have the following properties: both preserve the so-called Idown Set; then, F exchanges the two statistics Major Index and Inversion Number, while G exchanges the Down Set with its complement to n. Several applications are given, in particular further properties of the Robinson correspondence between permutations and pairs of Young tableaux.

foata@unistra.fr

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