幻方的几个充要条件  

Some Necessary and Sufficient Conditions of Magic Squares

作　　者：张世德[1] 李程 张迪 

机构地区：[1]河南师范大学数学与信息科学学院,河南新乡453007 [2]河南大象网络技术有限公司,河南郑州450002 [3]美亚财产保险有限公司广东分公司,广东广州510045

出　　处：《数学的实践与认识》2016年第4期198-214,共17页Mathematics in Practice and Theory

摘　　要：建立等重方阵的概念,并运用它阐述幻方、2次幻方、3次幻方及中心对称互补幻方的充要条件,根据这些结论构作出一些8阶、9阶2次中心对称互补幻方.In this paper, the concept of equal repetition matrix is introduced and the necessary and sufficient conditions of magic squares, quadratic magic squares, cubic magic squares and symmetrical complementary magic squares about the center are described by using such concept. Using these results some quadratic magic squares of orders 8 and 9 were constructed and they are all symmetrical complementary magic squares about the center.

关 键 词：等重方阵 中心对称互补方阵 对角拉丁方 对角拉丁方正交侣 幻方 

分 类 号：O151.21[理学—数学]