摘要
孙述寰等在文献[4]上给出了4阶强魔性幻方的定义,并求得4阶强魔性幻方总数及其中不同构的个数.我们引进了对偶矩阵和对偶变换的概念,并由此证明了5<sup>n</sup>阶强魔性幻方总数为（5<sup>n</sup>l）<sup>2</sup>C<sub>2n</sub><sup>n</sup>,其中不同构的为1/8（5<sup>n</sup>l）<sup>2</sup>C<sub>2n</sub><sup>n</sup>个。
In this paper some general theorems on magic squares of order 5' satisfying 'strong magic condition' (abbreviated as 'S. M. C') are obtained, which improve essentially Hugo S. H. Sun's results [4]. First we establish definitions on dual matrix having 'S. M. C'and dual transformation, then we prove that the total number of magic squares of order 5' having'S. M. C'is equal to (5n1 )2C2mm. in which (5n1)2C2nn/8 sguares are not isomorphic. The analysis depends on the new concepts of dual matrices and dual transformations.
出处
《杭州大学学报（自然科学版）》
CSCD
1994年第2期146-152,共7页
Journal of Hangzhou University Natural Science Edition
基金
浙江省教委科研基金资助课题
关键词
幻方
强魔性
对偶矩阵
对偶变换
magic squares
strong magic condition
dual matrix
dual transforma-tion
