A Generating Tree Approach to k-Nonnesting Partitions and Permutations

@article{Burrill2011AGT,
  title={A Generating Tree Approach to k-Nonnesting Partitions and Permutations},
  author={Sophie Burrill and S. Elizalde and M. Mishna and Li-Hsing Yen},
  journal={Annals of Combinatorics},
  year={2011},
  volume={20},
  pages={453-485}
}
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… Expand
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