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Avoiding Type or Patterns in a Partition of a Set

Toufik Mansour / Mark Shattuck
Published Online: 2012-08-01 | DOI: https://doi.org/10.1515/integers-2012-0004


A partition of the set is a collection of nonempty pairwise disjoint subsets of (called blocks) whose union equals . In this paper, we find exact formulas and/or generating functions for the number of partitions of with k blocks, where k is fixed, which avoid 3-letter patterns of type or , providing generalizations in several instances. In the particular cases of , , and , we are only able to find recurrences and functional equations satisfied by the generating function, since in these cases there does not appear to be a simple explicit formula for it.

Keywords: Set Partition; Pattern Avoidance; Stirling Number

About the article

Received: 2010-09-22

Accepted: 2012-02-23

Published Online: 2012-08-01

Published in Print: 2012-08-01

Citation Information: Integers, Volume 12, Issue 4, Pages 757–785, ISSN (Online) 1867-0652, ISSN (Print) 1867-0652, DOI: https://doi.org/10.1515/integers-2012-0004.

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© 2012 by Walter de Gruyter Berlin Boston.Get Permission

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