Fix-Mahonian Calculus, I: two transformations

Dominique Foata (1) , Guo-Niu Han (1)

1 IRMA - Institut de Recherche Mathématique Avancée

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.

Domaines: Combinatoire [math.CO]

Dominique Foata, Guo-Niu Han. Fix-Mahonian Calculus, I: two transformations. 2007. ⟨hal-00135868⟩