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Annals of Combinatorics

, Volume 20, Issue 3, pp 453–485 | Cite as

A Generating Tree Approach to k-Nonnesting Partitions and Permutations

  • Sophie Burrill
  • Sergi Elizalde
  • Marni Mishna
  • Lily Yen
Article

Abstract

We describe a generating tree approach to the enumeration and exhaustive generation of k-nonnesting set partitions and permutations. Unlike previous work in the literature which uses the connections of these objects to Young tableaux and restricted lattice walks, our approach deals directly with partition and permutation diagrams. We provide explicit functional equations for the generating functions, with k as a parameter. Key to the solution is a superset of diagrams that permit semi-arcs. Many of the resulting counting sequences also count other well-known objects, such as Baxter permutations, and Young tableaux of bounded height.

Mathematics Subject Classification

05A15 05A18 

Keywords

enumeration generating tree partition permutation nonnesting 

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  • Sophie Burrill
    • 1
  • Sergi Elizalde
    • 2
  • Marni Mishna
    • 1
  • Lily Yen
    • 1
    • 3
  1. 1.Department of MathematicsSimon Fraser UniversityBurnabyCanada
  2. 2.Department of MathematicsDartmouth CollegeHanoverUSA
  3. 3.Department of Mathematics and StatisticsCapilano UniversityNorth VancouverCanada

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