Galled trees are studied as a recombination model in population genetics. This class of phylogenetic networks is generalized into tree-child and galled network classes by relaxing a structural condition imposed on galled trees. We provide a solution to an open problem that is how to count and enumerate tree-child networks with fixed number of leaves and reticulations. Explicit counting formulas are also given for galled trees through their relationship to ordered trees and phylogenetic networks in which the child of each reticulation is a leaf.

中文翻译：

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计数和枚举树子网络及其子类

研究了枯萎的树木作为种群遗传学中​​的重组模型。通过放松施加在树木上的结构条件，将此类系统发育网络概括为树状子类别和树木状网络类别。我们提供了一个开放问题的解决方案，该问题是如何计算和枚举具有固定数量的叶子和网状结构的树状子网络。通过与树木有序的树木和系统发育网络的关系（其中每个网状结构的子项是叶子），还给出了树木的显式计数公式。