Set partitions with isolated successions

T Mansour, AO Munagi

Research output: Contribution to journalArticlepeer-review


We enumerate partitions of the set {1, ... , n} according to occurrences of isolated successions, that is, integer strings a, a + 1, ... , b in a block when neither a - 1 nor b + 1 lies in the same block. Our results include explicit formulas and generating functions for the number of partitions containing isolated successions of a given length. We also consider a corresponding analog of the associated Stirling numbers of the second kind.
Original languageAmerican English
Pages (from-to)81-91
Number of pages11
JournalNotes on Number Theory and Discrete Mathematics
Issue number1
StatePublished - 2022


  • Generating function
  • Isolated succession
  • Partition
  • Recurrence


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