Abstract : We study the enumeration of Dyck paths having a first return decomposition with special properties based on a height constraint. We exhibit new restricted sets of Dyck paths counted by the Motzkin numbers, and we give a constructive bijection between these objects and Motzkin paths. As a byproduct, we provide a generating function for the number of Motzkin paths of height k with a flat (resp. with no flats) at the maximal height. (C) 2018 Elsevier B.V. All rights reserved.
Keywords
KeyWords Plus:STATISTICS; STRINGS
https://hal-univ-bourgogne.archives-ouvertes.fr/hal-01860743
Contributeur : Le2i - Université de Bourgogne
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Soumis le : jeudi 23 août 2018 - 17:03:52
Dernière modification le : mercredi 8 janvier 2020 - 11:26:12
