Catalan numbers and pattern restricted set partitions

Toufik Mansour, Matthias Schork, Mark Shattuck

Research output: Contribution to journalArticlepeer-review


Suppose π=π1π2πn is a partition of size n, represented in its canonical sequential form. We show that the number of partitions of size n so represented having no two adjacent letters the same and avoiding a single pattern of length five is given by the Catalan number Cn-1 in six particular instances. In addition to supplying apparently new combinatorial structures counted by the Catalan numbers, this provides interesting examples of the more general question of enumerating how many members which belong to some class of words satisfying an adjacency requirement avoid a given subsequence pattern.

Original languageEnglish
Pages (from-to)2979-2991
Number of pages13
JournalDiscrete Mathematics
Issue number20
StatePublished - 28 Oct 2012


  • Catalan number
  • Pattern avoidance
  • Set partition

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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