Phylogenetic degrees for claw trees

IF 0.9 2区数学 Q2 MATHEMATICS

Journal of Combinatorial Theory Series A Pub Date : 2024-03-15 DOI:10.1016/j.jcta.2024.105886

Rodica Andreea Dinu , Martin Vodička

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引用次数: 0

Abstract

Group-based models appear in algebraic statistics as mathematical models coming from evolutionary biology, namely in the study of mutations of genomes. Motivated also by applications, we are interested in determining the algebraic degrees of the phylogenetic varieties coming from these models. These algebraic degrees are called phylogenetic degrees. In this paper, we compute the phylogenetic degree of the variety $X_{G, n}$ with $G \in {Z_{2}, Z_{2} \times Z_{2}, Z_{3}}$ and any n-claw tree. As these varieties are toric, computing their phylogenetic degree relies on computing the volume of their associated polytopes $P_{G, n}$ . We apply combinatorial methods and we give concrete formulas for these volumes.

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爪树的系统发生度

基于组的模型作为进化生物学的数学模型出现在代数统计学中，即基因组突变的研究中。同样是受应用的驱使，我们对确定这些模型产生的系统发育品种的代数度感兴趣。这些代数度被称为系统发生度。在本文中，我们将计算G∈{Z2,Z2×Z2,Z3}和任意n棵爪树的XG,n的系统发生度。由于这些多面体是环状的，计算它们的系统发生度依赖于计算它们相关的多面体 PG,n 的体积。我们运用组合方法，给出了这些体积的具体公式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Combinatorial Theory Series A 数学-数学

CiteScore

2.90

自引率

9.10%

发文量

审稿时长

12 months

期刊介绍： The Journal of Combinatorial Theory publishes original mathematical research concerned with theoretical and physical aspects of the study of finite and discrete structures in all branches of science. Series A is concerned primarily with structures, designs, and applications of combinatorics and is a valuable tool for mathematicians and computer scientists.