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Construction of Fair Dice Pairs

1
Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China
2
School of Mathematics and Big Data, Guizhou Education University, Guiyang 550018, China
3
Department of Mathematics, Shanghai University, Shanghai 200444, China
4
Department of Network Technology, South China Institute of Software Engineering, Guangzhou 510990, China
5
Department of Mathematics, Changzhou Institute of Technology, Changzhou 213022, China
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(5), 440; https://doi.org/10.3390/math7050440
Received: 8 April 2019 / Revised: 9 May 2019 / Accepted: 13 May 2019 / Published: 17 May 2019
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PDF [290 KB, uploaded 17 May 2019]

Abstract

An interesting and challenging problem in mathematics is how to construct fair dice pairs. In this paper, by means of decomposing polynomials in a residue class ring and applying the Discrete Fourier Transformation, we present all the 2000 fair dice pairs and their 8 equivalence classes in a four-person game, identifying what we call the mandarin duck property of fair dice pairs. View Full-Text
Keywords: fair dice pairs; discrete Fourier transformation; discrete convolution fair dice pairs; discrete Fourier transformation; discrete convolution
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Huang, Y.; Zeng, Z.; Rao, Y.; Zou, Y.; Wang, Y.; Huang, X. Construction of Fair Dice Pairs. Mathematics 2019, 7, 440.

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