Generating trees for partitions and permutations with no k-nestings†
نویسندگان
چکیده
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. Résumé. Nous décrivons une approche, basée sur l’utilisation d’arbres de génération, pour l’énumération et la génération exhaustive de partitions et permutations sans k-emboı̂tement. Contrairement aux travaux antérieurs qui reposent sur un lien entre ces objets, tableaux de Young et familles de chemins dans des treillis, notre approche traite directement partitions et diagrammes de permutations. Nous fournissons des équations fonctionnelles explicites pour les séries génératrices, avec k en tant que paramètre.
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