Multivariate generalizations of the Foata-Schutzenberger equidistribution

Details Multivariate generalizations of the Foata-Schutzenberger equidistribution Multivariate generalizations of the Foata-Schutzenberger equidistribution

2006-05-02

arxiv.org/abs/math/0605060v2

Mathematics

Combinatorics

17 pages, LaTex; Minor correction in the proof of Lemma 6.5; one reference added

Scientific paper

A result of Foata and Schutzenberger 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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