On the enumeration of rooted trees with fixed size of maximal decreasing trees

Details On the enumeration of rooted trees with fixed size of maximal decreasing trees On the enumeration of rooted trees with fixed size of maximal decreasing trees

2011-06-07

arxiv.org/abs/1106.1290v2

Mathematics

Combinatorics

10 pages, 1 figures

Scientific paper

10.1016/j.disc.2011.10.001

Let $\T_{n}$ be the set of rooted labeled trees on $\set{0,...,n}$. A maximal
decreasing subtree of a rooted labeled tree is defined by the maximal subtree
from the root with all edges being decreasing. In this paper, we study a new
refinement $\T_{n,k}$ of $\T_n$, which is the set of rooted labeled trees whose
maximal decreasing subtree has $k+1$ vertices.

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