Research on Reflection and Rotation Features of Binomial Coefficient Distributions

Zhu Minghan; Zheng Jeffrey Zhijie

doi:doi:10.11648/j.sd.20190704.21

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Research on Reflection and Rotation Features of Binomial Coefficient Distributions

Zhu Minghan, Zheng Jeffrey Zhijie

Published in Science Discovery (Volume 7, Issue 4)

Received: 8 July 2019 Published: 27 August 2019

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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.

Published in	Science Discovery (Volume 7, Issue 4)
DOI	10.11648/j.sd.20190704.21
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), 2019. Published by Science Publishing Group

Keywords

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

References

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[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.
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[15]	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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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

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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

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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

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@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://article.sciencepublishinggroup.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}
}

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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  -

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Author Information

Zhu Minghan

School of Software, Yunnan University, Kunming, China
Zheng Jeffrey Zhijie

Yunnan Laboratory of Quantum Information, Kunming, China

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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

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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

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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

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@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://article.sciencepublishinggroup.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