Science Discovery

| Peer-Reviewed |

Research on Reflection and Rotation Features of Binomial Coefficient Distributions

Received: 08 July 2019    Accepted:     Published: 27 August 2019
Views:       Downloads:

Share This Article

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.

DOI 10.11648/j.sd.20190704.21
Published in Science Discovery (Volume 7, Issue 4, August 2019)
Page(s) 239-248
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Binomial Coefficient, Spatial Extension, Variant Construction, Reflection, Rotation

References
[1] Brualdi,R.A. 组合数学(原书第4版)[M]. 机械工业出版社:2005。
[2] 庞兴梅. 组合变换在等式、多项式及简单图中的应用[D]. 天津:南开大学,2009。
[3] EvaPart-Enander. MATLAB 5手册[M]. 机械工业出版社:2000。
[4] Cleve Moler. Experiments with MATLAB[M]. 北京航空航天大学出版社:2013。
[5] 尹社会. 利用伯努利系数表计算刚体转动惯量[R].高师理科学刊,2012,32(3)。
[6] 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。
[7] Morgan.F. 几何测度论[M]. 世界图书出版公司,2009。
[8] 吴军.数学之美[M]. 人民邮电出版社, 2012。
[9] 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。
[10] 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
[11] 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.
[12] 赵熙强. Vandermonde卷积公式统一形式及其相应超几何变换[J]大连理工大学学报, 2000, 40(6)。
[13] 逯志宇. 基于对称旋转不变性的非圆相干分布源直接定位算法[J]电子与信息学报, 2019,41(3)。
[14] 王庆平. 计量逻辑学中的反射变换[J]模糊系统与数学, 2018,32(6)。
[15] Kumar V. B. Efficient Computation of Binomial Coefficients Using Splay Trees [J]. International Journal on Data Science and Technology, 2016, 2 (1)。
Author Information
  • School of Software, Yunnan University, Kunming, China

  • Yunnan Laboratory of Quantum Information, Kunming, China

Cite This Article
  • APA Style

    Zhu Minghan, Zheng Jeffrey Zhijie. (2019). Research on Reflection and Rotation Features of Binomial Coefficient Distributions. Science Discovery, 7(4), 239-248. https://doi.org/10.11648/j.sd.20190704.21

    Copy | Download

    ACS Style

    Zhu Minghan; Zheng Jeffrey Zhijie. Research on Reflection and Rotation Features of Binomial Coefficient Distributions. Sci. Discov. 2019, 7(4), 239-248. doi: 10.11648/j.sd.20190704.21

    Copy | Download

    AMA Style

    Zhu Minghan, Zheng Jeffrey Zhijie. Research on Reflection and Rotation Features of Binomial Coefficient Distributions. Sci Discov. 2019;7(4):239-248. doi: 10.11648/j.sd.20190704.21

    Copy | Download

  • @article{10.11648/j.sd.20190704.21,
      author = {Zhu Minghan and Zheng Jeffrey Zhijie},
      title = {Research on Reflection and Rotation Features of Binomial Coefficient Distributions},
      journal = {Science Discovery},
      volume = {7},
      number = {4},
      pages = {239-248},
      doi = {10.11648/j.sd.20190704.21},
      url = {https://doi.org/10.11648/j.sd.20190704.21},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.sd.20190704.21},
      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.},
     year = {2019}
    }
    

    Copy | Download

  • TY  - JOUR
    T1  - Research on Reflection and Rotation Features of Binomial Coefficient Distributions
    AU  - Zhu Minghan
    AU  - Zheng Jeffrey Zhijie
    Y1  - 2019/08/27
    PY  - 2019
    N1  - https://doi.org/10.11648/j.sd.20190704.21
    DO  - 10.11648/j.sd.20190704.21
    T2  - Science Discovery
    JF  - Science Discovery
    JO  - Science Discovery
    SP  - 239
    EP  - 248
    PB  - Science Publishing Group
    SN  - 2331-0650
    UR  - https://doi.org/10.11648/j.sd.20190704.21
    AB  - 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.
    VL  - 7
    IS  - 4
    ER  - 

    Copy | Download

  • Sections