ANALYSIS OF COMBINATORIAL CODING NUMBERS OF THE GENETIC CODE PATTERNS
遗传密码格式的组合编码数分析

The coding pattern which uses N codons to encode m objects is a vertex in N dimension space of m elements. The combinatorial coding number of 64 codons to encode 20 amino acids and the terminate code is very huge. The topological properties of the polynomial high dimension spaces (the m-N spaces) were first analyzed and the characteristic triangles (Chen Weichang Triangles) of the m-N spaces were obtained. A mathematical proof of the characteristic triangles was also given. Obviously, the coding pattern of the genetic code is a vertex in a 64 dimension space of 21 elements. Using the combinatorial mathematical method, the following combinatorial numbers of genetic coding patterns had been calculated: the maximum combinatorial number of genetic coding patterns Cm(Cm=4.19×1084); the combinatorial number of genomic coding pattens CG(CG=1.13×1080, the combinatorial number of mitochondrial coding patterns CT(CT=1.38×1079. It is suggested that the determination of the genetic code is an event of extremely small probability. The origin of the genomic genetic codes might be from the symmetry breaking of the triplets pairs of the mitochondrial codes.