Counting subwords in a partition of a set

Toufik Mansour, Mark Shattuck, Sherry H.F. Yan

Research output: Contribution to journalArticlepeer-review


A partition π of the set [n] = {1, 2,...,n} is a collection {B1,...,Bk} of nonempty disjoint subsets of [n] (called blocks) whose union equals [n]. In this paper, we find explicit formulas for the generating functions for the number of partitions of [n] containing exactly k blocks where k is fixed according to the number of occurrences of a subword pattern for several classes of patterns, including all words of length 3. In addition, we find simple explicit formulas for the total number of occurrences of the patterns in question within all the partitions of [n] containing k blocks, providing both algebraic and combinatorial proofs.

Original languageEnglish
Pages (from-to)1-21
Number of pages21
JournalElectronic Journal of Combinatorics
Issue number1
StatePublished - 2010

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics
  • Applied Mathematics


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