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Research on Reflection and Rotation Features of Binomial Coefficient Distributions
Science Discovery
Volume 7, Issue 4, August 2019, Pages: 239-248
Received: Jul. 8, 2019; Published: Aug. 27, 2019
Authors
Zhu Minghan, School of Software, Yunnan University, Kunming, China
Zheng Jeffrey Zhijie, Yunnan Laboratory of Quantum Information, Kunming, China
Article Tools Abstract PDF (1178KB)
Abstract
With the rapid development of frontier neural network, artificial intelligence and big data technology, the related theory and application research of combinatorial mathematics are more and more extensive. The application of binomial coefficient in combinatorial mathematics is an effective way to solve the research of information coding and quantum computation. Binomial coefficients and its distributions are the core topic in probability statistics, and there are many theories and applications related to them.In this paper, the quantification of binomial coefficients and the characteristic of reflection rotation transformation are studied using three-dimensional diagrams. Using variant construction, the combinatorial clustering properties are investigated applying binomial formulas and sample distributions and their combinatorial patterns are illustrated. It is proved that the basic binomial coefficient formula and its extended model have obvious properties of reflection and rotation invariance.
Keywords
Binomial Coefficient, Spatial Extension, Variant Construction, Reflection, Rotation
Zhu Minghan, Zheng Jeffrey Zhijie, Research on Reflection and Rotation Features of Binomial Coefficient Distributions, Science Discovery. Vol. 7, No. 4, 2019, pp. 239-248. doi: 10.11648/j.sd.20190704.21
References

Brualdi,R.A. 组合数学（原书第4版）[M]. 机械工业出版社:2005。



EvaPart-Enander. MATLAB 5手册[M]. 机械工业出版社：2000。

Cleve Moler. Experiments with MATLAB[M]. 北京航空航天大学出版社:2013。



Knuth.D.E. 计算机编程的艺术(第4卷:组合算法,第1部分)[M]. 国防工业出版社，2011。

Morgan.F. 几何测度论[M]. 世界图书出版公司，2009。



Knuth.D.E. 计算机编程的艺术（第1卷，第3版）[M]. 国防工业出版社，2002。

ZHENG Jeffrey Z. J. Variant Construction From Theoretical Foundations To Applications [M]. China: Springer, 2019: 39-50, 237-245. https://link.springer.com/book/10.1007/978-981-13-2282-2

ZHENG Jeffrey Z. J. A framework to express variant and invariant functional spaces for binary logic [J]. Front. Electr. Electron. Eng. China 5 (2), 163–172 (2010). Higher Educational Press and Springer.







Kumar V. B. Efficient Computation of Binomial Coefficients Using Splay Trees [J]. International Journal on Data Science and Technology, 2016, 2 (1)。
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