On two subclasses of Motzkin paths and their relation to ternary trees
Combinatorics
2019-02-06 v1
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.
Cite
@article{arxiv.1902.01681,
title = {On two subclasses of Motzkin paths and their relation to ternary trees},
author = {Helmut Prodinger and Sarah J. Selkirk and Stephan Wagner},
journal= {arXiv preprint arXiv:1902.01681},
year = {2019}
}
Comments
This is a very extended version of arXiv:1808.01907