【摘要】 在不改变对角方阵各行、各列、主对角线、次对角线的元素之集的条件下,其变换群是n次对称群S_n的直积S_n×S_n的子群,因对角拉丁方、对角拉丁方正交侣、幻方、高次幻方、加乘幻方均属此类方阵,本文对构作这类对象及研究它们的计数有重要意义.更多还原

【Abstract】 In this paper,we show that the transformaion group of diagonal square matrices is a subgroup of direct product S_n×S_n of symetric groups of order n,if the sets of elements of each row,each column and the two diagonals are kept constant,respectively.The diagonal Latin squares,pair of orthogonal daigonal Latin squares,magic squares,magic squares of high dgree,addition multiplacation magic squares are diagonal square matrices.This paper plays an important role in the study of construction and enumeration of the objects above.更多还原