Counting Tree-Child Networks and Their Subclasses

计数樱桃缩减序列就是计数线性扩展（在系统发育树子网络中）

Counting cherry reduction sequences is counting linear extensions (in phylogenetic tree-child networks)

本文证明在系统发育树子网络中计数樱桃与网状樱桃缩减序列数量等价于计数网络诱导偏序集的线性扩展，并提出了一个复杂度受网络层级约束的算法。

树-子网络的排名计数

Counting rankings of tree-child networks

本文研究了树-子网络排名的计数问题，探讨了其与正常网络的关系，并给出了随机选择的树-子网络排名数量的渐进行表达式。

A Short Note on the Exact Counting of Tree-Child Networks

Tree-child networks are an important network class which are used in phylogenetics to model reticulate evolution. In a recent paper, Pons and Batle (2021) conjectured a relation between tree-child networks and certain words. In this short note, we prove their conjecture for the (important) class of one-component tree-child networks.

计数树-子网络的Pons-Batle恒等式的一个简短组合证明

A Short Combinatorial Proof of the Pons-Batle Identity for Counting Tree-Child Networks

针对计数树-子网络的Pons-Batle恒等式，本文给出一个简短的组合证明，明确了相关网络数目满足的递推关系。

二元系统发育网络的渐近计数

Asymptotic Counting of Binary Phylogenetic Networks

研究在n个分类群上具有k个网状结构的二元系统发育网络的渐近计数，其中k随n增长，通过边插入分析局部结构，证明当k=o(√n)时，网络数量渐近于二项式系数乘以指数形式。

Generating Normal Networks via Leaf Insertion and Nearest Neighbor Interchange

Galled trees are studied as a recombination model in theoretic population genetics. This class of phylogenetic networks has been generalized to tree-child networks, normal networks and tree-based networks by relaxing a structural condition. Although these networks are simple, their topological structures have yet to be fully understood. It is well-known that all phylogenetic trees on $n$ taxa can be generated by the insertion of the $n$-th taxa to each edge of all the phylogenetic trees on $n-1$ taxa. We prove that all tree-child networks with $k$ reticulate nodes on $n$ taxa can be uniquely g…