Catalan numbers and pattern restricted set partitions

Toufik Mansour; Matthias Schork; Mark Shattuck

doi:https://doi.org/10.1016/j.disc.2012.06.021

Catalan numbers and pattern restricted set partitions

Toufik Mansour, Matthias Schork, Mark Shattuck

Department of Mathematics

University of Haifa

Research output: Contribution to journal › Article › peer-review

Abstract

Suppose π=^π1π2⋯^πn 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 language	American English
Pages (from-to)	2979-2991
Number of pages	13
Journal	Discrete Mathematics
Volume	312
Issue number	20
DOIs	https://doi.org/10.1016/j.disc.2012.06.021
State	Published - 28 Oct 2012

Keywords

Catalan number
Pattern avoidance
Set partition

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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https://doi.org/10.1016/j.disc.2012.06.021

Cite this

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AU - Shattuck, Mark

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N2 - Suppose π=π1π2⋯πn 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.

AB - Suppose π=π1π2⋯πn 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.

KW - Catalan number

KW - Pattern avoidance

KW - Set partition

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DO - https://doi.org/10.1016/j.disc.2012.06.021

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JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 20

ER -

Catalan numbers and pattern restricted set partitions

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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