特殊四阶幻方的变换群

The Transformation Groups of Special Magic Squares of Order Four

本篇文章考虑了特殊四阶幻方的变换群及幻方分类的问题。通过研究特殊四阶幻方的变换,结合对称群中的置换元素相互作用生成的轮换关系,给出了192阶和384阶变换群。接着利用变换群将特殊四阶幻方进一步分成了不同形式的9类,辅助于计算机程序可以搜索到具体结果。

In this paper, the transformation groups of special magic squares of order 4 and the classification of magic squares are considered. We will manifest the existence of the transformation groups of order 192 and 384 by studying the transformations and rotation relations. Then we divide the special magic squares into different 9 classes under the action of given transformation groups. By making use of the computer programmer, the precise data can be searched.