摘要
就调和正交拉丁方的存在性进行了探讨,给出了调和性的几何意义及调和数Hn=1/4b·(n+1)^2的理论解释;构作了阶为9,25和49的调和正交拉丁方的具体实例。
This paper discusses the existance of harmonically orthogonal latin squares.A geometrical explanation of harmonicity and two representations of the special number H_n=1/4n·(n+ 1)~2(called harmonic number)are given.Examples of harmonically orthogonal latin squares of order 9,25,49 are constructed.
关键词
对角拉丁方
正交拉丁方
调和正交拉丁方
拉丁方
Diagonal latin square
Orthogonal latin square
Harmonic number
Harmonically orthogonal latin square