马氏不变量与四叉树的迷向子群
Markov invariants and the isotropy subgroup of a quartet tree
摘要：
本文的目的是展示如何在二叉树上的叶排列的各向同性子组可以被用来系统地识别树信息不变量相关的系统发育进化模型。在四重奏的情况下，我们给出了一个明确的建设的全套表示，并描述其性质。我们将这些结果直接应用到马尔可夫不变量，从而扩展了以前的理论结果，系统地确定线性组合消失，为一个给定的四重奏。我们还注意到，该理论是完全可推广到任意树，也同样适用于系统发育不变量的相关情况。所有的结果遵循有限群的表示论的基本考虑。
英文摘要：
The purpose of this article is to show how the isotropy subgroup of leaf permutations on binary trees can be used to systematically identify tree-informative invariants relevant to models of phylogenetic evolution. In the quartet case, we give an explicit construction of the full set of representations and describe their properties. We apply these results directly to Markov invariants, thereby extending previous theoretical results by systematically identifying linear combinations that vanish for a given quartet. We also note that the theory is fully generalizable to arbitrary trees and is equally applicable to the related case of phylogenetic invariants. All results follow from elementary consideration of the representation theory of finite groups.
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