完美置换和空间均衡拉丁方

郑豪, 曹海涛

数学学报 ›› 2022, Vol. 65 ›› Issue (5) : 939-950.

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中国科学院数学与系统科学研究院期刊网
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数学学报 ›› 2022, Vol. 65 ›› Issue (5) : 939-950. DOI: 10.12386/A20210055
论文

完美置换和空间均衡拉丁方

    郑豪, 曹海涛
作者信息 +

Perfect Permutations and Spatially Balanced Latin Squares

    Hao ZHENG, Hai Tao CAO
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文章历史 +

摘要

本文首次提出完美置换的概念并研究它的代数性质和构造方法，解决了2n+1为素数时n阶完美置换的存在性.我们还利用完美置换给出了循环空间均衡拉丁方和对称空间均衡拉丁方的构造方法，它们在试验设计中有广泛的应用.

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.

关键词

完美置换 / 循环拉丁方 / 对称拉丁方 / 空间均衡拉丁方

Key words

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

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郑豪, 曹海涛. 完美置换和空间均衡拉丁方. 数学学报, 2022, 65(5): 939-950 https://doi.org/10.12386/A20210055
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

参考文献

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基金

国家自然科学基金（12071226，11931006）；国家自然科学青年基金（11901039）资助项目
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