Fix-Mahonian Calculus, I: two transformations
Combinatorics
2007-05-23 v1
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.
Keywords
Cite
@article{arxiv.math/0703099,
title = {Fix-Mahonian Calculus, I: two transformations},
author = {Dominique Foata and Guo-Niu Han},
journal= {arXiv preprint arXiv:math/0703099},
year = {2007}
}