Let $\mathcal{ O}_n$ be the set of ordered labeled trees on ${ 0,...,n}$. A maximal decreasing subtree of an ordered labeled tree is defined by the maximal ordered subtree from the root with all edges being decreasing. In this paper, we study a new refinement $\mathcal{ O}_{ n,k}$ of $\mathcal{ O}_n$, which is the set of ordered labeled trees whose maximal decreasing subtree has $k+1$ vertices.
Categories: math.CO