矩阵遗传学，第1部分：三联体位置排列和遗传矩阵的对称性
Matrix genetics, part 1: permutations of positions in triplets and symmetries of genetic matrices
摘要：
研究了遗传矩阵的Kronecker族，它是基于遗传矩阵[CT; AG]，其中C，T，A，G是遗传字母表中的字母.矩阵[CT; AG]的二次克罗内克幂是（4*4）-矩阵的16个对偶。矩阵[C T; A G]的三次克罗内克幂是64个三元组的（8*8）-矩阵。重要的是，遗传密码简并性的特点反映在这些遗传矩阵的对称黑白马赛克中。本文介绍了这些镶嵌矩阵的有趣的数学性质，它们与双联体和三联体内的位置排列、投影算子、酉矩阵和循环群等有关。分形遗传网络被认为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新的对称性原理的一些结果。
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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