Dyck paths with a first return decomposition constrained by height

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
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Soumis le : jeudi 23 août 2018 - 17:03:52
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Jean-Luc Baril, Sergey Kirgizov, Armen Petrossian. Dyck paths with a first return decomposition constrained by height. Discrete Mathematics, Elsevier, 2018, 341 (6), pp.1620 - 1628. ⟨10.1016/j.disc.2018.03.002⟩. ⟨hal-01860743⟩



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