Weighted unary-binary trees, Hex-trees, marked ordered trees, and related structures
Combinatorics
2021-08-24 v2
Abstract
Hex-trees are identified as a particular instance of weighted unary-binary trees. The Horton-Strahler numbers of these objects are revisited, and, thanks to a substitution that is not immediately intuitive, explicit results are possible. They are augmented by asymptotic evaluations as well. Furthermore, marked ordered trees (in bijection to skew Dyck paths) are investigated, followed 3-Motzkin paths and multi-edge trees. The underlying theme is sequence A002212 in the Encyclopedia of integer sequences.
Cite
@article{arxiv.2106.14782,
title = {Weighted unary-binary trees, Hex-trees, marked ordered trees, and related structures},
author = {Helmut Prodinger},
journal= {arXiv preprint arXiv:2106.14782},
year = {2021}
}
Comments
Title has changed. Material from arXiv:2105.03350 has been included, together with new material