A note on plane trees with decreasing labels

Abstract

This note derives asymptotic upper and lower bounds for the number of planted plane trees on $n$ nodes assigned labels from the set $\{1,2,\dots ,k\}$ 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.

9 pages, 2 figures