Existence of strongly symmetrical weakly pandiagonal graeco-latin squares
A graeco-latin sauare is a pair of orthogonal latin squares. It is a design of experiment in which the experimental units are grouped in three different ways. In this paper, constructions of a pair of orthogonal latin sauares which are both strongly symmetrical and weakly pandiagonal are investigate...
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| Format: | Article |
| Language: | English |
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De Gruyter
2018-09-01
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| Series: | Special Matrices |
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| Online Access: | https://doi.org/10.1515/spma-2018-0013 |
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doaj-cc61622fcb054f09af81722bd642b5f92021-10-02T18:54:20ZengDe GruyterSpecial Matrices2300-74512018-09-016135736810.1515/spma-2018-0013spma-2018-0013Existence of strongly symmetrical weakly pandiagonal graeco-latin squaresZhang Yong0Chen Kejun1Li Wen2School of Mathematics and Statistics, Yancheng Teachers University,Jiangsu, P. R., ChinaSchool of Mathematics and Information Science, Nanjing Normal University of Special Education, Nanjing,Jiangsu, P. R., ChinaSchool of Science, Xichang University,Sichuan, P. R., ChinaA graeco-latin sauare is a pair of orthogonal latin squares. It is a design of experiment in which the experimental units are grouped in three different ways. In this paper, constructions of a pair of orthogonal latin sauares which are both strongly symmetrical and weakly pandiagonal are investigated. As a result, it is proved that there exists a pair of strongly symmetrical weakly pandiagonal orthogonal latin sauare of order n if and only if n > 4 and n ≡ 0, 1, 3 (mod 4) with only one possible exception for n = 12.https://doi.org/10.1515/spma-2018-0013latin squaregraecoorthogonalstrongly symmetricalweakly pandiagonal |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Zhang Yong Chen Kejun Li Wen |
| spellingShingle |
Zhang Yong Chen Kejun Li Wen Existence of strongly symmetrical weakly pandiagonal graeco-latin squares Special Matrices latin square graeco orthogonal strongly symmetrical weakly pandiagonal |
| author_facet |
Zhang Yong Chen Kejun Li Wen |
| author_sort |
Zhang Yong |
| title |
Existence of strongly symmetrical weakly pandiagonal graeco-latin squares |
| title_short |
Existence of strongly symmetrical weakly pandiagonal graeco-latin squares |
| title_full |
Existence of strongly symmetrical weakly pandiagonal graeco-latin squares |
| title_fullStr |
Existence of strongly symmetrical weakly pandiagonal graeco-latin squares |
| title_full_unstemmed |
Existence of strongly symmetrical weakly pandiagonal graeco-latin squares |
| title_sort |
existence of strongly symmetrical weakly pandiagonal graeco-latin squares |
| publisher |
De Gruyter |
| series |
Special Matrices |
| issn |
2300-7451 |
| publishDate |
2018-09-01 |
| description |
A graeco-latin sauare is a pair of orthogonal latin squares. It is a design of experiment in which the experimental units are grouped in three different ways. In this paper, constructions of a pair of orthogonal latin sauares which are both strongly symmetrical and weakly pandiagonal are investigated. As a result, it is proved that there exists a pair of strongly symmetrical weakly pandiagonal orthogonal latin sauare of order n if and only if n > 4 and n ≡ 0, 1, 3 (mod 4) with only one possible exception for n = 12. |
| topic |
latin square graeco orthogonal strongly symmetrical weakly pandiagonal |
| url |
https://doi.org/10.1515/spma-2018-0013 |
| work_keys_str_mv |
AT zhangyong existenceofstronglysymmetricalweaklypandiagonalgraecolatinsquares AT chenkejun existenceofstronglysymmetricalweaklypandiagonalgraecolatinsquares AT liwen existenceofstronglysymmetricalweaklypandiagonalgraecolatinsquares |
| _version_ |
1716848602157940736 |