A refined enumeration of $p$-ary labeled trees

Abstract

Let ${\mathcal{T}}_n^{(p)}$ be the set of $p$-ary labeled trees on $\{1,2,\dots ,n\}$. A maximal decreasing subtree of an $p$-ary labeled tree is defined by the maximal $p$-ary subtree from the root with all edges being decreasing. In this paper, we study a new refinement ${\mathcal{T}}_{n,k}^{(p)}$ of ${\mathcal{T}}_n^{(p)}$, which is the set of $p$-ary labeled trees whose maximal decreasing subtree has $k$ vertices.

7 pages, 4 figures, 2 tables

References in corpus (2)

• A Generalized Enumeration of Labeled Trees and Reverse Prüfer Algorithm
• On the enumeration of rooted trees with fixed size of maximal decreasing trees