Labeled Partitions and the q-Derangement Numbers

Details Labeled Partitions and the q-Derangement Numbers Labeled Partitions and the q-Derangement Numbers

2006-06-20

arxiv.org/abs/math/0606481v1

Mathematics

Combinatorics

6 pages

Scientific paper

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.

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