Fix-Mahonian Calculus III; a Quadruple Distribution
Combinatorics
2007-05-23 v1
Abstract
A four-variable distribution on permutations is derived, with two dual combinatorial interpretations. The first one includes the number of fixed points "fix", the second the so-called "pix" statistic. This shows that the duality between derangements and desarrangements can be extended to the case of multivariable statistics. Several specializations are obtained, including the joint distribution of (des, exc), where "des" and "exc" stand for the number of descents and excedances, respectively.
Keywords
Cite
@article{arxiv.math/0703454,
title = {Fix-Mahonian Calculus III; a Quadruple Distribution},
author = {Dominique Foata and Guo-Niu Han},
journal= {arXiv preprint arXiv:math/0703454},
year = {2007}
}
Comments
26 pages