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arXiv · 1902.01681

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

Helmut Prodinger·Sarah J. Selkirk·Stephan Wagner
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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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Helmut Prodinger, Sarah J. Selkirk, Stephan Wagner. 2019-02-05. On two subclasses of Motzkin paths and their relation to ternary trees. https://arxiv.org/abs/1902.01681

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