基于变值测量对三项式组合系数的多维可视化探索
Multidimensional Visualization Exploration of Trinomial Combination Coef-ficient Based on Variant Measurement

DOI: 10.12677/SA.2019.84080, PP. 704-710

Keywords: 变值测量，组合数，可视化，三项式组合系数
Variable Measurement, Combination Number, Visualization, Trinomial Coefficient

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Abstract:

二项式、三项式组合计数的计算在概率统计、人工智能、大数据等的数据描述和分析中起着核心作用。本文利用变值测量，对三项式组合计数系数的多维分布进行计算和投影。采用二项式组合表达式和四元变值度量为基础，对二项式组合系数进行分解转换，形成三项式组合系数表达式，利用组合数计算方法得到二维量化计数矩阵。将相关数值计算结果转化为统计二维直方图，以二维彩图模式展现。文中利用多个图示结果展现出三项式系数的空间对称性和分布多样性的特征。从三项式组合系数分布的变化和不变特性，系统地探索各种组合变换的聚类分布特性。
The binomial and trinomial combination counting calculation mode plays a core role in data description and data analysis of probability statistics, artificial intelligence, and big data. In this paper, the variable measurement is used to calculate and project the multi-dimensional distribution of the trinomial combination counting coefficient. Based on the binomial combination equation and the quaternary variable metric, the binomial combination coefficients are decomposed and transformed to form a trinomial combination coefficient equation, and the two-dimensional quantization counting matrix is obtained by the combination number calculation method. The relevant numerical calculation results are converted into statistical two-dimensional histograms and displayed in a two-dimensional color map. In this paper, the results of spatial symmetry and distribution diversity of the trinomial coefficients are exhibited by using multiple graphical results. From the variation and invariant characteristics of the trinomial combination coefficient distribution, the clustering distribution characteristics of various combined transformations are systematically explored.

References

[1]	宋桢桢, 及万会. 由裂项法导出二项式系数级数[J]. 西南民族大学学报(自然科学版), 2013, 39(5): 709-717.
[2]	毛经中. 组合数学基础[M]. 武汉: 华中师范大学出版社, 1990.
[3]	Hall, M. (1986) Combinatorial Theory. 2nd Edition, Wiley Interscience, New York.
[4]	Chen, J.R. (2012) Combinatorial Mathematics. Harbin Institute of Technology Press, Harbin.
[5]	Gould, H.W. (1972) Combinatorial Identities. Morgantown Printing and Binding Company, Morganton.
[6]	Stanton, D. and White, D. (1986) Constructive Combinatorics. Springer, New York. https://doi.org/10.1007/978-1-4612-4968-9
[7]	李秦. 基于Matlab的数学可视化问题研究及实践[J]. 兰州交通大学学报, 2013, 32(4): 27-30.
[8]	郑智捷, 郑昊航. 变值测量结构及其可视化统计分布[J]. 光子学报, 2011, 40(9): 1397-1404.
[9]	Zheng, J. (2011) Conditional Probability Statistical Distributions in Variant Measurement Simulations. Acta Photonica Sinica, 40, 1662-1666. https://doi.org/10.3788/gzxb20114011.1662
[10]	郑智捷. 多元逻辑函数的基础等价变值表示[J]. 云南民族大学学报(自然科学版), 2011, 20(5): 396-397.
[11]	Knuth, D.E. (1998) Art of Computer Programming, the: Volume 1: Fundamental Algorithms, 3rd Edition. China Machine Press, Beijing.
[12]	Gould, H.W. (1956) Some Generalizations of Vandermonde’s Convolution. American Mathematical Monthly, 63, 84-91. https://doi.org/10.1080/00029890.1956.11988763
[13]	Zheng, J. (2019) Variant Logic Construction under Permutation and Complementary Operations on Binary Logic. In: Zheng, J., Ed., Variant Construction from Theoretical Foundation to Applications, Springer, Singapore, 3-21. https://doi.org/10.1007/978-981-13-2282-2_1

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