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Generating trees for partitions and permutations with no k-nestings
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012), DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) (2012) Cet article a éte moissonné depuis la source Episciences

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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 using 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. 
@article{DMTCS_2012_special_263_a36,
     author = {Burrill, Sophie and Elizalde, Sergi and Mishna, Marni and Yen, Lily},
     title = {Generating trees for partitions and permutations with no k-nestings},
     journal = {Discrete mathematics & theoretical computer science},
     year = {2012},
     volume = {DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)},
     doi = {10.46298/dmtcs.3050},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3050/}
}
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%D 2012
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Burrill, Sophie; Elizalde, Sergi; Mishna, Marni; Yen, Lily. Generating trees for partitions and permutations with no k-nestings. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012), DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) (2012). doi: 10.46298/dmtcs.3050

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