Labeled Partitions and the q-Derangement Numbers
Combinatorics
2007-05-23 v1
Abstract
By a re-examination of MacMahon's original proof of his celebrated theorem on the distribution of the major indices over permutations, we give a reformulation of his argument in terms of the structure of labeled partitions. In this framework, we are able to establish a decomposition theorem for labeled partitions that leads to a simple bijective proof of Wachs' formula on the q-derangement numbers.
Keywords
Cite
@article{arxiv.math/0606481,
title = {Labeled Partitions and the q-Derangement Numbers},
author = {William Y. C. Chen and Deheng Xu},
journal= {arXiv preprint arXiv:math/0606481},
year = {2007}
}
Comments
6 pages