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Discrete Mathematics & Theoretical Computer Science |
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.
Source : ScholeXplorer
IsRelatedTo ARXIV 1806.08306 Source : ScholeXplorer IsRelatedTo DOI 10.1016/j.aim.2019.106732 Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.1806.08306
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