Florent Hivert ; Jean-Christophe Novelli ; Jean-Yves Thibon - Multivariate generalizations of the Foata-Schützenberger equidistribution

dmtcs:3511 - Discrete Mathematics & Theoretical Computer Science, January 1, 2006, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities - https://doi.org/10.46298/dmtcs.3511
Multivariate generalizations of the Foata-Schützenberger equidistributionArticle

Authors: Florent Hivert ORCID1; Jean-Christophe Novelli 2; Jean-Yves Thibon ORCID2

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.


Volume: DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities
Section: Proceedings
Published on: January 1, 2006
Imported on: May 10, 2017
Keywords: permutation,inversion,descent,[INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]
Funding:
    Source : HAL
  • Algèbres de Hopf combinatoires, opérades et props; Funder: French National Research Agency (ANR); Code: ANR-06-BLAN-0380

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