摘要翻译：
提出了多字母遗传学的概念。用矩阵形式表示分子遗传字母表的多级系统，揭示了该系统的代数性质。这些性质与众所周知的并矢群和并矢移位矩阵的概念有关。矩阵遗传学研究了遗传字母表与某些类型的超复数，包括对偶数和双复合数及其扩展之间的关系。在螺旋理论和斐波那契矩阵的基础上，提出了一种新的方法来模拟生物螺旋和叶序规律的遗传遗传现象。构建了全人类基因组三胞胎子集的并矢树。在遗传矩阵的基础上，提出了内补方阵的新概念。本文描述了这类矩阵研究的初步结果。我们的结果证明了生命物质具有深刻的代数本质。他们展示了发展代数生物学的新的有希望的方法。
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英文标题：
《Dyadic groups, dyadic trees and symmetries in long nucleotide sequences》
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作者：
Sergey V. Petoukhov
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最新提交年份：
2013
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分类信息：

一级分类：Quantitative Biology        数量生物学
二级分类：Other Quantitative Biology        其他定量生物学
分类描述：Work in quantitative biology that does not fit into the other q-bio classifications
不适合其他q-bio分类的定量生物学工作
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英文摘要：
  The conception of multi-alphabetical genetics is represented. Matrix forms of the representation of the multi-level system of molecular-genetic alphabets have revealed algebraic properties of this system. These properties are connected with well-known notions of dyadic groups and dyadic-shift matrices. Matrix genetics shows relations of the genetic alphabets with some types of hypercomplex numbers including dual numbers and bicomplex numbers together with their extensions. A possibility of new approach is mentioned to simulate genetically inherited phenomena of biological spirals and phyllotaxis laws on the base of screw theory and Fibonacci matrices. Dyadic trees for sub-sets of triplets of the whole human genome are constructed. A new notion is put forward about square matrices with internal complementarities on the base of genetic matrices. Initial results of the study of such matrices are described. Our results testify that living matter possesses a profound algebraic essence. They show new promising ways to develop algebraic biology.
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PDF链接：
https://arxiv.org/pdf/1204.6247