Dyck paths with a first return decomposition constrained by height

Jean-Luc Baril (1) , Sergey Kirgizov (1) , Armen Petrossian (1)

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

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

Mots clés: Enumeration; Dyck and Motzkin paths; First return decomposition; Statistics; Height; Peak; Strings

Domaines: Mathématiques [math]

Jean-Luc Baril, Sergey Kirgizov, Armen Petrossian. Dyck paths with a first return decomposition constrained by height. Discrete Mathematics, 2018, 341 (6), pp.1620 - 1628. ⟨10.1016/j.disc.2018.03.002⟩. ⟨hal-01860743⟩