论文标题
关于用任意节点的列出叶片标记的增加树木
On the enumeration of leaf-labelled increasing trees with arbitrary node-degree
论文作者
论文摘要
我们考虑\ textit {叶片标记的增加树的数量的计数问题，其中内部节点可能具有任意数量的后代。所有此类树木的集合是在某些人群基础模型（例如多合并结合体）中获得的家谱的离散表示。尽管二进制树的组合学却众所周知，但对于所有树木的数量，仅知道近似渐近公式。在这项工作中，我们将此公式验证为恒定的术语，并比较所有叶片标记的树木数量的渐近行为与二元，三元和第四纪树的树木的数量。
We consider the counting problem of the number of \textit{leaf-labeled increasing trees}, where internal nodes may have an arbitrary number of descendants. The set of all such trees is a discrete representation of the genealogies obtained under certain population-genetical models such as multiple-merger coalescents. While the combinatorics of the binary trees among those are well understood, for the number of all trees only an approximate asymptotic formula is known. In this work, we validate this formula up to constant terms and compare the asymptotic behavior of the number of all leaf-labelled increasing trees to that of binary, ternary and quaternary trees.
