Fix-Mahonian Calculus, I: two transformations

Details Fix-Mahonian Calculus, I: two transformations Fix-Mahonian Calculus, I: two transformations

2007-03-04

arxiv.org/abs/math/0703099v1

Mathematics

Combinatorics

Scientific paper

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.

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