用对换阵构造幻方的充要条件

THE NECESSARY AND SUFFICIENT CONDITION FOR MAKING MAGIC SQUARE BY MATRIX OF TRANSPOSITION

自1988年本文作者之一提出用正交对换阵构造偶数阶幻方之后,最近几年又有一些学者推广了这一方法,用来构造奇数阶幻方,但是,迄今为止,所有的论文都只是提供了种种的构造幻方的充分条件,本文则在对换的范围内提出了一个简明的充要条件(定理5),所以,本文实际上是对1988年以来幻方理论的发展所作的一个全面总结,

In 1988,the first author of this paper published a paper on 'making even order magic squares by orthogonal matrix of transposition'. Since then,some scholars have spread this method so far as to use it to make odd order magic squares. However,all the papers published up to now have only given different kinds of sufficient conditions for making magic squares. This paper in troduces a brief necessary and sufficient condition ABD(Theorem 5)in the domain of transposition. Therefore,in fact, this paper is a full suming—up of the development of magic square theory since 1988.