论文标题
$ d $ combining tree-child网络的枚举
Enumeration of $d$-combining Tree-Child Networks
论文作者
论文摘要
树木网络是用于建模包含网状事件的进化过程的最突出的网络类之一。最近的一些研究解决了{\ it双组养树网络}的计数问题，这些问题是养树网络的网络，每个网状节点都有两个父母。在本文中，我们将这些研究扩展到{\ it $ d $ combining Tree-Child Networks}，每个网状节点现在都有$ d \ geq 2 $父母。此外，我们还为网络的网状节点数量的分布行为提供了结果和猜想，该分布行为是从所有叶子数量相同数量的树木网络集合中随机绘制的。
Tree-child networks are one of the most prominent network classes for modeling evolutionary processes which contain reticulation events. Several recent studies have addressed counting questions for {\it bicombining tree-child networks} which are tree-child networks with every reticulation node having exactly two parents. In this paper, we extend these studies to {\it $d$-combining tree-child networks} where every reticulation node has now $d\geq 2$ parents. Moreover, we also give results and conjectures on the distributional behavior of the number of reticulation nodes of a network which is drawn uniformly at random from the set of all tree-child networks with the same number of leaves.
