Á¦¸ñ / Enumeration of labeled trees
ÃÊ·Ï / Let ${\mathcal T}_{n}$ be the set of
rooted labeled trees on
$\set{0,...,n}$.
Given a rooted labeled tree $T$, A maximal decreasing
subtree of a rooted labeled tree
is defined by the maximal subtree
from the root with all edges being decreasing. Recently Seo and Shin
have studied a new refinement ${\mathcal
T}_{n,k}$ of ${\mathcal
T}_n$, which is the set of rooted labeled trees whose maximal
decreasing subtree has $k+1$ vertices.
In this talk, we introduce the
refinement of the set of labeled ordered trees by the size of
maximal
decreasing trees. We also present a refinement of the set of
labeled
$p$-ary trees. This is a joint work with Heesung Shin.