A note on plane trees with decreasing labels
Combinatorics
2026-03-04 v1
Abstract
This note derives asymptotic upper and lower bounds for the number of planted plane trees on nodes assigned labels from the set with the restriction that on any path from the root to a leaf, the labels must strictly decrease. We illustrate an application to calculating the largest eigenvalue of the adjacency matrix of a tree.
Keywords
Cite
@article{arxiv.2502.14596,
title = {A note on plane trees with decreasing labels},
author = {Tsun-Ming Cheung and Luc Devroye and Marcel K. Goh},
journal= {arXiv preprint arXiv:2502.14596},
year = {2026}
}
Comments
9 pages, 2 figures