对角方阵的变换群  

Transformaion Group of Diagonal Square Matrices

作　　者：张世德[1] 李程 

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

出　　处：《数学的实践与认识》2011年第11期162-170,共9页Mathematics in Practice and Theory

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.In this paper,we show that the transformaion group of diagonal square matrices is a subgroup of direct product Sn × Sn 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.

关 键 词：群 群的直积 对称群 对角拉丁方 对角拉丁方正交侣 幻方 高次幻方 

分 类 号：O152.1[理学—数学]