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Existence of Yang Hui Type Magic Squares

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Abstract

In this paper, some constructions of Yang Hui type magic squares are provided. As their application, it is shown that there exists a Yang Hui type magic square YMS\((n,2)\) for all even order \(n\ge 4\). Meanwhile, a diagonally ordered irrational YMS\((n,2)\) is also mentioned and it is shown that such a YMS\((n,2)\) exists for all integers \(n\equiv 2\pmod 4\) with \(n\ge 6\).

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Acknowledgments

The authors would like to thank Professor L. Zhu of Suzhou University for helpful discussions. The authors would like to thank W. Li of Sichuang Province for his example of YMS\((10,2)\).

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Authors and Affiliations

  1. Department of Mathematics, Taizhou University, Jiangsu, 225300, China

    Nanyuan Cao & Kejun Chen

  2. Department of Mathematics, Yancheng Teachers University, Jiangsu, 224002, China

    Yong Zhang

Authors
  1. Nanyuan Cao
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  2. Kejun Chen
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  3. Yong Zhang
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Corresponding author

Correspondence to Kejun Chen.

Additional information

The research is supported by the NNSFCs (No. 11371308 and No. 11301457).

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Cao, N., Chen, K. & Zhang, Y. Existence of Yang Hui Type Magic Squares. Graphs and Combinatorics 31, 1289–1310 (2015). https://doi.org/10.1007/s00373-014-1480-7

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  • DOI: https://doi.org/10.1007/s00373-014-1480-7

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