Set Partitions with No m-Nesting

Conference paper

Abstract

A partition of \(\{1,\ldots,n\}\) has an m-nesting if it contains at least m disjoint blocks, and a subset of 2m points \(i_{1} < i_{2} <\ldots < i_{m} < j_{m} < j_{m-1} <\ldots < j_{1}\), such that i l and j l are in the same block for all 1 ≤ lm, but no other pairs are in the same block. In this note, we use generating trees to construct the class of partitions with no m-nesting, determine functional equations satisfied by the associated generating functions, and generate enumerative data for m ≥ 4.

Keywords

Set partition Nesting Pattern avoidance Generating tree Algebraic kernel method Coefficient extraction Enumeration 

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Notes

Acknowledgements

We are grateful to an anonymous referee for many constructive suggestions, to Mireille Bousquet-Mélou for her suggestions, and to Mogens Lemvig Hansen for his tireless generation of numbers with Maple. The first author is partially supported by an Natural Sciences and Engineering Research Council of Canada Discovery Grant.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of MathematicsSimon Fraser UniversityBurnabyCanada
  2. 2.Department of Mathematics and StatisticsCapilano UniversityNorth VancouverCanada

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