Statistics on ordered partitions of sets

Details Statistics on ordered partitions of sets Statistics on ordered partitions of sets

2006-05-26

arxiv.org/abs/math/0605670v4

Mathematics

Combinatorics

Added footnote on first page explaining relation to work of others

Scientific paper

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.

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