On the enumeration of rooted trees with fixed size of maximal decreasing trees
arXiv:1106.1290 · doi:10.1016/j.disc.2011.10.001
Abstract
Let $\T_{n}$ be the set of rooted labeled trees on . 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 vertices.
10 pages, 1 figures