NoteCounting humps in Motzkin paths
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Highlights
► We give a bijection between humps of Motzkin paths and super-Motzkin paths. ► Using this bijection we count the number of humps in all Motzkin paths of order . ► We give a new proof that the number of Dyck paths of order with peaks is the Narayana number. ► We also count the number of humps in Schröder paths, and get a combinatorial proof of an identity.
Keywords
Dyck paths
Motzkin paths
Schröder paths
Humps
Peaks
Narayana number
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