Einar Steingrimsson
Published 2006-05-26, updated 2014-09-02Version 5
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.
Comments: Corrected typos in a name, insignificant to the mathematical content
A $q,r$-analogue of poly-Stirling numbers of second kind with combinatorial applications
Stirling numbers for complex reflection groups
Set partitions with no m-nesting
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