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Multivariate generalizations of the Foata-Schützenberger equidistribution

Abstract : 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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Florent Hivert, Jean-Christophe Novelli, Jean-Yves Thibon. Multivariate generalizations of the Foata-Schützenberger equidistribution. Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, 2006, Nancy, France. pp.289-300, ⟨10.46298/dmtcs.3511⟩. ⟨hal-01184716⟩

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