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arXiv · 1106.1290

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

Seunghyun Seo·Heesung Shin
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Abstract

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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Seunghyun Seo, Heesung Shin. 2012-01-02. On the enumeration of rooted trees with fixed size of maximal decreasing trees. https://doi.org/10.1016/j.disc.2011.10.001

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