Multivariate generalizations of the Foata-Schützenberger equidistribution
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,...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2006-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/3511/pdf |
| Summary: | 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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| ISSN: | 1365-8050 |