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一类强对称自正交对角数独的存在性

Existence of a family of strongly symmetric self-orthogonal diagonal Sudoku squares
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摘要 研究了强对称自正交对角数独,引申了Lorch的构造方法,利用有限域上的线性空间理论给出了基本构造,证明了:对所有奇素数p,存在一个p2阶强对称自正交对角数独. Strongly symmetric self-orthogonal diagonal Sudoku square is investigated. The construction used by Lorch is extended via linear space over finite field, and a construction of such a Sudoku square is obtained. It is proved that a strongly symmetric self-orthogonal diagonal Sudoku square of order n exists when n is an odd prime integer.
作者 邵旭彦 张勇 王成敏
机构地区 江南大学理学院 盐城师范学院数学与统计学院
出处 《高校应用数学学报（A辑）》 CSCD 北大核心 2015年第4期469-475,共7页 Applied Mathematics A Journal of Chinese Universities(Ser.A)
基金 国家自然科学基金(11301457 11371308 11471144)
关键词 数独 拉丁方 自正交 强对称 对角 Sudoku square Latin square self-orthogonal strongly symmetric diagonal
分类号 O157.2 [理学—基础数学]
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参考文献13

  • 1Colbourn C J, Dinitz J H, eds. Handbook of Combinatorial Designs[M]. 2nd Edition, BocaRaton: Chapman and Hall/CRC, 2007.
  • 2Keedwell A D. On Sudoku squares[J]. Bull Inst Combin Appl, 2007, 50: 52 - 60.
  • 3Keedwell A D. Constructions of complete sets of orthogonal diagonal Sudoku squares[J].Austral J Combin, 2010,47(1): 227-238.
  • 4Lorch J. Mutually orthogonal families of linear sudoku Solutions[J]. J Austral Math Soc,2009,87: 409-420.
  • 5Lorch J. Orthogonal combings of linear Sudoku solutions [J]. Austral. J Combin, 2010, 47(1):247-264.
  • 6Lorch J. A quick construction of mutually orthogonal Sudoku squares [J]. arXiv: 1303.0411[math.CO], 2013.
  • 7Pedersen R M, Vis T L. Sets of mutually orthogonal Sudoku latin squres[J]. College Math.J. 2009, 40: 174-180.
  • 8Danhof K J, Phillips N C K, Wallis W D. On self-orthogonal diagonal Latin squares [J]. JCombin Math Combin Comput, 1990, 8: 3-8.
  • 9Du Beiliang. On the existence of self-orthogonal diagonal Latin squares[J]. Australas JCombin, 1994, 10: 45-50.
  • 10Bennett F E, Du Beiliang, Zhang Hangtao. Existence of self-orthogonal diagonal Latinsquares with a missing subsquare[J]. Discrete Math, 2003,261: 69-86.

二级参考文献5

  • 1[1]Danhof K J, Phillips N C K, Wallis W D. On Self-orthogonal Diagonal Latin Squares. J. Combin. Math. Combin. Comput., 1990, 8:3-8
  • 2[2]Heinrich K, Wu L, Zhu L. Incomplete Self-orthogonal Latin Squares ISOLS(6m+6,2m) Exist for all m. Discrete Math., 1991, 87:281-290
  • 3[3]Heinrich K, Zhu L. Incomplete Self-orthogonal Latin Squares. J. Austral. Math. Soc. (Series A),1987, 42:365-384
  • 4[4]Zhu L. Existence of Self-orthogonal Latin Squares ISOLS(6m+2,2m). Ars Combin., 1995, 39:65-74
  • 5[5]Bragton R B, Coppersmith D, Hoffman A J. Self-orthogonal Latin Squares. Teorie Combinatoric,Proc. Rome Conf., 1976, 509-517
高校应用数学学报（A辑）
2015年 第4期

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