Statistics on ordered partitions of sets

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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.
Original languageEnglish
Pages (from-to)557-574
Number of pages18
JournalJournal of Combinatorics
Issue number3
Publication statusPublished - 11 May 2020


  • ordered set partitions
  • q-Stirling numbers
  • permutation statistics


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