Dyck paths with a first return decomposition constrained by height |
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Authors: | Jean-Luc Baril Sergey Kirgizov Armen Petrossian |
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Affiliation: | LE2I UMR-CNRS 6306, Université de Bourgogne, B.P. 47 870, 21078 DIJON-Cedex, France |
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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 with a flat (resp. with no flats) at the maximal height. |
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Keywords: | Enumeration Dyck and Motzkin paths First return decomposition Statistics Height Peak |
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