Construction of Fair Dice Pairs
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-pe...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-05-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/7/5/440 |
| _version_ | 1818189228680413184 |
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| author | Yong Huang Zhenbing Zeng Yongsheng Rao Yu Zou Ying Wang Xing Huang |
| author_facet | Yong Huang Zhenbing Zeng Yongsheng Rao Yu Zou Ying Wang Xing Huang |
| author_sort | Yong Huang |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-11T23:39:29Z |
| format | Article |
| id | doaj.art-1a7f2431f79c492196a677f55f4d848a |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-11T23:39:29Z |
| publishDate | 2019-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-1a7f2431f79c492196a677f55f4d848a2022-12-22T00:45:46ZengMDPI AGMathematics2227-73902019-05-017544010.3390/math7050440math7050440Construction of Fair Dice PairsYong Huang0Zhenbing Zeng1Yongsheng Rao2Yu Zou3Ying Wang4Xing Huang5Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, ChinaDepartment of Mathematics, Shanghai University, Shanghai 200444, ChinaInstitute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, ChinaInstitute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, ChinaDepartment of Network Technology, South China Institute of Software Engineering, Guangzhou 510990, ChinaDepartment of Mathematics, Changzhou Institute of Technology, Changzhou 213022, ChinaAn 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.https://www.mdpi.com/2227-7390/7/5/440fair dice pairsdiscrete Fourier transformationdiscrete convolution |
| spellingShingle | Yong Huang Zhenbing Zeng Yongsheng Rao Yu Zou Ying Wang Xing Huang Construction of Fair Dice Pairs Mathematics fair dice pairs discrete Fourier transformation discrete convolution |
| title | Construction of Fair Dice Pairs |
| title_full | Construction of Fair Dice Pairs |
| title_fullStr | Construction of Fair Dice Pairs |
| title_full_unstemmed | Construction of Fair Dice Pairs |
| title_short | Construction of Fair Dice Pairs |
| title_sort | construction of fair dice pairs |
| topic | fair dice pairs discrete Fourier transformation discrete convolution |
| url | https://www.mdpi.com/2227-7390/7/5/440 |
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