Abstract
The application of binomial coefficient in combinatorial mathematics is an effective way to solve the problem of information coding and quantum computation. Binomial coefficient and its distribution are the core topics in probability statistics. In this paper, binomial coefficient formula is used to show the special wave effect by transforming the model of parameters and forming the relation with reflection and symmetry. The quantization of binomial coefficients and the characteristics of reflection rotation transformation were studied by using 2d histogram visualization. From the perspective of global invariance, the structures of binomial coefficients and their combined clustering properties are systematically investigated. Compared with the standard normal distribution and the fluctuation effect distribution, the fluctuation effect of binomial formula formed by variable value measurement is shown. Using the wave effect shown by the binomial coefficient formula constructed in this paper to simulate the physical nanoscale optics, quantum information science, computer science to lay a theoretical foundation and provide a new method.
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