Geodesic
Multivariate generalizations of the Foata-Schützenberger equidistribution
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities (2006).

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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. 
@article{DMTCS_2006_special_252_a35,
     author = {Hivert, Florent and Novelli, Jean-Christophe and Thibon, Jean-Yves},
     title = {Multivariate generalizations of the {Foata-Sch\"utzenberger} equidistribution},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities},
     year = {2006},
     doi = {10.46298/dmtcs.3511},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3511/}
}
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%J Discrete mathematics & theoretical computer science
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Hivert, Florent; Novelli, Jean-Christophe; Thibon, Jean-Yves. Multivariate generalizations of the Foata-Schützenberger equidistribution. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities (2006). doi : 10.46298/dmtcs.3511. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3511/

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