On two subclasses of Motzkin paths and their relation to ternary trees

2019/02/05 by Helmut Prodinger, Prodinger, Helmut, Sarah J. Selkirk +3
Computer Science · Mathematics · #05A15 #05A19 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1902.01681

openalex publication_date 2019/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Two subclasses of Motzkin paths, S-Motzkin and T-Motzkin paths, are introduced. We provide bijections between S-Motzkin paths and ternary trees, S-Motzkin paths and non-crossing trees, and T-Motzkin paths and ordered pairs of ternary trees. Symbolic equations for both paths, and thus generating functions for the paths, are provided. Using these, various parameters involving the two paths are analyzed.

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