摘要翻译：
研究了基于遗传矩阵[C T；A G]的Kronecker族遗传矩阵，其中C,T,A,G是遗传字母表的字母。第二次Kronecker幂中的矩阵[C T；A G]是16个重复的(4*4)-矩阵。第三次Kronecker幂中的矩阵[C T；A G]是64个三元组的(8*8)-矩阵。重要的是，遗传密码的退化特性反映在这些遗传矩阵的对称黑白镶嵌中。本文给出了这些镶嵌矩阵的有趣的数学性质，这些镶嵌矩阵与二重体和三重体中的位置排列有关；投影仪操作员；分形遗传网络具有酉矩阵、循环群等特点，是研究长核苷酸序列的一种新的有效工具。描述了揭示长核苷酸序列对称性新原理的一些结果。
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英文标题：
《Matrix genetics, part 1: permutations of positions in triplets and
  symmetries of genetic matrices》
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作者：
Sergey V. Petoukhov (Department of Biomechanics, Mechanical
  Engineering Research Institute of the Russian Academy of Sciences)
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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 Kronecker family of the genetic matrices is investigated, which is based on the genetic matrix [C T; A G], where C, T, A, G are the letters of the genetic alphabet. The matrix [C T; A G] in the second Kronecker power is the (4*4)-matrix of 16 duplets. The matrix [C T; A G] in the third Kronecker power is the (8*8)-matrix of 64 triplets. It is significant that peculiarities of the degeneracy of the genetic code are reflected in the symmetrical black-and-white mosaic of these genetic matrices. The article represents interesting mathematical properties of these mosaic matrices, which are connected with positional permutations inside duplets and triplets; with projector operators; with unitary matrices and cyclic groups, etc. Fractal genetic nets are proposed as a new effective tool to study long nucleotide sequences. Some results about revealing new symmetry principles of long nucleotide sequences are described.
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PDF链接：
https://arxiv.org/pdf/0803.0888