English

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 nn nodes assigned labels from the set {1,2,,k}\{1,2,\ldots, k\} 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

R2 v1 2026-06-28T21:51:24.870Z