Dyck paths with a first return decomposition constrained by height

Jean-Luc Baril; Sergey Kirgizov; Armen Petrossian

doi:10.1016/j.disc.2018.03.002

Article dans une revue

Dyck paths with a first return decomposition constrained by height

Jean-Luc Baril ^{1, *} Sergey Kirgizov ¹ Armen Petrossian ¹

* Auteur correspondant

1 Le2i - Laboratoire d'Electronique, d'Informatique et d'Image [EA 7508]

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

Keywords : Enumeration Dyck and Motzkin paths First return decomposition Statistics Height Peak Strings

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Article dans une revue

Domaine :

Mathématiques [math]

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https://hal-univ-bourgogne.archives-ouvertes.fr/hal-01860743
Contributeur : Le2i - Université de Bourgogne <>
Soumis le : jeudi 23 août 2018 - 17:03:52
Dernière modification le : vendredi 17 juillet 2020 - 14:59:10

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