一般有腔树、时间一致有腔树和简单时间一致有腔树的组合比较
Combinatorial comparison of general galled trees, time-consistent galled trees, and simplex time-consistent galled trees
AI总结：
本文比较了三种有腔树类别的组合特性，发现固定回路数时一般有腔树与时间一致有腔树数量相同，而简单时间一致有腔树更少，且在无限制回路数时三者数量递减。
摘要：
根部二元系统发育网络是根部二元树的扩展，增加了用于表示涉及杂交事件的进化过程的回路节点。枚举组合学研究已经对各种类别的叶标记系统发育网络进行了计数，发现当回路数量固定时，时间一致有腔树在数量上渐近上少于之前检查过的几种网络类别。在这里，我们提供了对两种额外网络类别的枚举结果：一般有腔树和简单时间一致有腔树。我们显示，当回路数量固定时，随着叶数趋于无穷大，一般有腔树的渐近计数与时间一致有腔树相同，而简单时间一致有腔树的计数更小。如果回路数量不受限制，则渐近近似值都不同：简单时间一致有腔树比时间一致有腔树少，而时间一致有腔树又比一般有腔树少。我们还报告了各种其他结果：用于计数具有少量叶和固定回路数量的网络的递推式，以及在我们研究的类别中无标记网络的枚举结果。
英文摘要：
Rooted binary phylogenetic networks are extensions of rooted binary trees, adding reticulation nodes that are designed to represent evolutionary processes that involve hybridization events. Enumerative combinatorics studies have counted leaf-labeled phylogenetic networks in a variety of classes, finding that when the number of reticulations is fixed, the time-consistent galled trees are asymptotically less numerous than each of several network classes that had been previously examined. Here we provide enumerative results on two additional network classes: general galled trees and simplex time-consistent galled trees. We show that for a fixed number of galls, as the number of leaves goes to infinity, the asymptotic count of general galled trees is identical to that of time-consistent galled trees, whereas the count of simplex time-consistent galled trees is smaller. If the number of galls is not restricted, then the asymptotic approximations all differ: simplex time-consistent galled trees are less numerous than time-consistent galled trees, which are in turn less numerous than general galled trees. We also report a variety of additional results: recursions to count the studied networks with small numbers of leaves a fixed number of galls, as well as enumerative results for unlabeled networks in the classes that we investigate.
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