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A refined enumeration of $p$-ary labeled trees

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 Added by Heesung Shin
 Publication date 2013
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and research's language is English




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Let $mathcal{T}^{(p)}_n$ be the set of $p$-ary labeled trees on ${1,2,dots,n}$. A maximal decreasing subtree of an $p$-ary labeled tree is defined by the maximal $p$-ary subtree from the root with all edges being decreasing. In this paper, we study a new refinement $mathcal{T}^{(p)}_{n,k}$ of $mathcal{T}^{(p)}_n$, which is the set of $p$-ary labeled trees whose maximal decreasing subtree has $k$ vertices.



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171 - Heesung Shin , Jiang Zeng 2010
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