Perfect Permutations and Spatially Balanced Latin Squares

Hao ZHENG, Hai Tao CAO

Acta Mathematica Sinica, Chinese Series ›› 2022, Vol. 65 ›› Issue (5) : 939-950.

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Acta Mathematica Sinica, Chinese Series ›› 2022, Vol. 65 ›› Issue (5) : 939-950. DOI: 10.12386/A20210055

Perfect Permutations and Spatially Balanced Latin Squares

  • Hao ZHENG, Hai Tao CAO
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Abstract

In this paper, a new conception called perfect permutation will be introduced. We focus on its algebraic properties and construction methods. The main result is that there exists a perfect permutation of order n when 2n + 1 is a prime. Furthermore, we use perfect permutations to construct cyclic spatially balanced Latin squares and symmetric spatially balanced Latin squares both of which are widely used in experimental designs.

Key words

perfect permutation / cyclic Latin square / symmetric Latin square / spatially balanced Latin square

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Hao ZHENG, Hai Tao CAO. Perfect Permutations and Spatially Balanced Latin Squares. Acta Mathematica Sinica, Chinese Series, 2022, 65(5): 939-950 https://doi.org/10.12386/A20210055

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