编码和排序X-cactus
Encoding and ordering X-cactuses
摘要：
系统发生网络是进化树或系统发育树的推广，通常用于表示相互交叉的物种的进化。一种特殊类型的系统发生网络是{ \em $X$ -cactus}，它本质上是一个仙人掌图，其中所有度小于3的顶点都被至少一个来自物种集合$X$的元素标记。在本文中，我们提出了一种{ \em编码} $X$ -仙人掌的方法，在某些集合的分区自然产生的$X$的$X$ -仙人掌。使用这种编码，我们还介绍了一个偏序集的$X$ -仙人掌（同构），并得出一些结构性质的偏序集。这包括分析其最小上界和最大下界的一些性质。我们的结果不仅将系统发育树的一些基本性质推广到$X$ -仙人掌上，而且为解决系统发育网络理论中的热点问题（如一致性网络的推导）提供了一种新的方法.
英文摘要：
Phylogenetic networks are a generalization of evolutionary or phylogenetic trees that are commonly used to represent the evolution of species which cross with one another. A special type of phylogenetic network is an {\em $X$-cactus}, which is essentially a cactus graph in which all vertices with degree less than three are labelled by at least one element from a set $X$ of species. In this paper, we present a way to {\em encode} $X$-cactuses in terms of certain collections of partitions of $X$ that naturally arise from $X$-cactuses. Using this encoding, we also introduce a partial order on the set of $X$-cactuses (up to isomorphism), and derive some structural properties of the resulting partially ordered set. This includes an analysis of some properties of its least upper and greatest lower bounds. Our results not only extend some fundamental properties of phylogenetic trees to $X$-cactuses, but also provides a new approach to solving topical problems in phylogenetic network theory such as deriving consensus networks.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
