Statistics on ordered partitions of sets
Combinatorics
2019-04-26 v6
Abstract
We introduce several statistics on ordered partitions of sets, that is, set partitions where the blocks are permuted arbitrarily. The distribution of these statistics is closely related to the q-Stirling numbers of the second kind. Some of the statistics are generalizations of known statistics on set partitions, but others are entirely new. All the new ones are sums of two statistics, inspired by statistics on permutations, where one of the two statistics is based on a certain partial ordering of the blocks of a partition.
Keywords
Cite
@article{arxiv.math/0605670,
title = {Statistics on ordered partitions of sets},
author = {Einar Steingrimsson},
journal= {arXiv preprint arXiv:math/0605670},
year = {2019}
}
Comments
Added a Prologue, as this paper is soon to be published in a journal