Bijections for Dyck paths with all peak heights of the same parity

2017/02/20 by Callan, David · 1 citation
#05A15 #05A19 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1702.06150

Abstract

We show bijectively that Dyck paths with all peaks at odd height are counted by the Motzkin numbers and Dyck paths with all peaks at even height are counted by the Riordan numbers.

Cited by

• Meanders and Dyck-Path Billiards

Related

• Some results on Dyck paths and Motzkin paths
• Counting Humps in Motzkin paths
• Two Bijections for Dyck Path Parameters
• Enumerations of humps and peaks in (k,a)-paths and (n,m)-Dyck paths via bijective proofs
• Counting peaks at height k in a Dyck path