Retakh's Motzkin paths and some combinatorial comments

2020/06/08 by Helmut Prodinger, Prodinger, Helmut
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2006.04977

openalex publication_date 2020/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Dyck paths where peaks are only allowed on level 1 and on even-indexed levels, were introduced by Retakh and analysed by Zeilberger, with assistance from Ekhad. We add some combinatorial comments to the enumeration, which involves Motzkin numbers, in particular, about the average height of such objects.

Citations

• Singularity Analysis of Generating Functions

Related

• Bijections for Dyck paths with all peak heights of the same parity
• Counting Humps in Motzkin paths
• Partial Skew Motzkin Paths
• Peakless Motzkin paths of bounded height
• Partial Motzkin paths with air pockets of the first kind avoiding peaks, valleys or double rises