摘要
纵横图是个古老的组合数学问题。本文以1～n^2个连续自然数构成的，l行、n列的方形阵列作为，l阶纵横图的基数字阵列，研究了其结构特点与纵横图特征（各行、各列及对角线数字和相等）的关系，提出了一种编制任意阶纵横图的通用性方法——对偶数字交换法。应用举例表明，该方法使用便易，不受纵横图的阶数约束，而且易于衍生出诸多种新的纵横图来。
A new method making up magic square is presented by analyzing the relation between the structure of n × n natural numbers array and the basic characteristic of any order magic square. The method is as follow： n/2 digitals of all dual rows or dual columns will be interchanged. If n is odd, adjusting the structure of the array is necessary, that is, the ordered series of numbers on the reverse first diagonal angle line, on the second diagonal line, on the central column and on the central row should be replaced respectively by the central column, the central row, the first diagonal angel line and the second diagonal angel line in the new array. Finally, some examples are given to show the advantage of this method, and many new kinds of magic squares will be generated by using this method.
出处
《山东大学学报（理学版）》
CAS
CSCD
北大核心
2014年第12期76-80,共5页
Journal of Shandong University(Natural Science)
关键词
纵横图
纵横图编制方法
对偶行间数字交换
对偶列间数字交换
对角数字交换
混合数字交换
magic square
method making up magic square
interchanging digitals between the dual rows in one column
interchanging digitals between the dual one row
interchanging digitals on the diagonal angel line
hybrid digital switching
