矩阵平移积和强魔性幻方

Matrix Translation Product and Magic Squares

本文给出了强魔性对偶矩阵和矩阵平移积的新概念;研究了这类矩阵的计数问题。并由此,通过对偶变换探讨阶P^n强魔性幻方的计数问题,(P为系数,n≥1)。文献[4]的结果是本文的一个例子。

Some new concepts on strong magic dual matrix and matrix translation product are given and counting problem of these matrices are then studied. In particular, the total number of strong magic squares of order pn(p being a prime number and n≥1) is calculated by using dual transformation, which explains that the results in [4] are special examples of this paper.