Multivariate generalizations of the Foata-Schützenberger equidistribution

@inproceedings{Hivert2006MultivariateGO,
  title={Multivariate generalizations of the Foata-Sch{\"u}tzenberger equidistribution},
  author={Florent Hivert and Jean-Christophe Novelli and Jean-Yves Thibon},
  year={2006}
}
A result of Foata and Schützenberger states that two statistics on permutations, the number of inversions and the inverse major index, have the same distribution on a descent class. We give a multivariate generalization of this property: the sorted vectors of the Lehmer code, of the inverse majcode, and of a new code (the inverse saillance code), have the same distribution on a descent class, and their common multivariate generating function is a flagged ribbon Schur function. 

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