Multivariate generalizations of the Foata-Schutzenberger equidistribution
Combinatorics
2007-05-23 v2
Abstract
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.
Keywords
Cite
@article{arxiv.math/0605060,
title = {Multivariate generalizations of the Foata-Schutzenberger equidistribution},
author = {F. Hivert and J. -C. Novelli and J. -Y. Thibon},
journal= {arXiv preprint arXiv:math/0605060},
year = {2007}
}
Comments
17 pages, LaTex; Minor correction in the proof of Lemma 6.5; one reference added