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The isometry group of phylogenetic tree space is 𝑆_{𝑛}
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2020-07-20 , DOI: 10.1090/proc/15154 Gillian Grindstaff
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2020-07-20 , DOI: 10.1090/proc/15154 Gillian Grindstaff
Abstract:A phylogenetic tree is an acyclic graph with distinctly labeled leaves whose internal edges have a positive weight. Given a set 
of 
leaves, the collection of all phylogenetic trees with this leaf set can be assembled into a metric cube complex known as phylogenetic tree space, or Billera-Holmes-Vogtmann tree space. In this largely combinatorial paper, we show that the isometry group of this space is the symmetric group 
. This fact is relevant to the analysis of some statistical tests of phylogenetic trees, such as those introduced in Testing to distinguish measures on metric spaces, preprint, 1802.01152, 2018.
中文翻译：
系统发育树空间的等距群是𝑆_{𝑛}
摘要：系统发育树是一个无环图，具有明显标记的叶子，其内部边缘的权重为正。给定一组的叶子，用这种叶集的所有进化树的集合可以组装成称为进化树空间，或Billera -福尔摩斯Vogtmann树空间度量立方体复杂。在这份很大程度上是组合的论文中，我们证明了该空间的等距群是对称群。这一事实与对系统发育树的一些统计测试的分析有关，例如在《区分度量空间度量的测试》（预印本，1802.01152，2018）中引入的统计测试。
更新日期：2020-09-01
of leaves, the collection of all phylogenetic trees with this leaf set can be assembled into a metric cube complex known as phylogenetic tree space, or Billera-Holmes-Vogtmann tree space. In this largely combinatorial paper, we show that the isometry group of this space is the symmetric group . This fact is relevant to the analysis of some statistical tests of phylogenetic trees, such as those introduced in Testing to distinguish measures on metric spaces, preprint, 1802.01152, 2018. 中文翻译：
系统发育树空间的等距群是𝑆_{𝑛}
摘要：系统发育树是一个无环图，具有明显标记的叶子，其内部边缘的权重为正。给定一组的叶子，用这种叶集的所有进化树的集合可以组装成称为进化树空间，或Billera -福尔摩斯Vogtmann树空间度量立方体复杂。在这份很大程度上是组合的论文中，我们证明了该空间的等距群是对称群。这一事实与对系统发育树的一些统计测试的分析有关，例如在《区分度量空间度量的测试》（预印本，1802.01152，2018）中引入的统计测试。
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