奇数阶幻方、泛对角线幻方构作数集的拓广  

Extension of Number Set Constructing Magic Squares and Pandiagona l Magic Squares of Order Odd

作　　者：张世德[1] 王俊卿[2] 朱红莺 

机构地区：[1]河南师范大学数学与信息科学学院,新乡453002 [2]中原工学院基础部 [3]南海市建设工程造价管理站

出　　处：《河南师范大学学报（自然科学版）》2001年第2期9-15,共7页Journal of Henan Normal University(Natural Science Edition)

基　　金：河南省科委自然科学基金资助课题

摘　　要：本文提出偏差分均匀矩阵、有心偏差分均匀矩阵、3等分偏差分均匀矩阵的概念 ,证明凡构成 2m +1(m≥ 1)阶有心偏差分均匀方阵的数集 ,均可构成 2m +1阶幻方 ;构成 6m +1(m ≥ 1) ,6m +5 (m ≥ 0 ) 阶偏差分均匀方阵的数集 ,均可构成相应阶的泛对角线幻方 ;构成 6m+3(m≥ 1) 阶 3等分偏差分均匀方阵的数集 ,均可构成 6m+3阶泛对角线幻方 .因偏差分对称矩阵是有心偏差分均匀矩阵的特例 ,因而本文将构成奇数阶幻方、n =6m +1、6m+5 阶泛对角线幻方的数集拓广为目前最为广泛的范围 ;n=6m+3的情况 ,偏差分对称矩阵与 3等分偏差分均匀矩阵是交叉概念 。This paper gave the concepts of matrix with uniform partial difference ,centered matrix with uniform partial difference ,trisection matrix with uniform p artial difference.It proves that:number set constructing centered matrix with uniform partial difference of order n=2m+1(m≥1) also constents magic squares of order n. Number set constructing matrix with uniform partial difference of orde r n=6m+1 or 6m+5 constents pandiagonal magic squares of order n respectively.Because number set constructing matrix with symetric partial difference is cente red matrix with uniform partial difference,this paper extended number set constr ucting magic squares and pandiagonal magic squares of order 6m+1 and 6m+5.The number set constructing trisection matrix with uniform partial difference of ord er 6m+3 constents pandiagonal magic squares of order 6m+3. Matrix with uniform partial difference and trisection matrix with uniform partial difference are cross concepts for n=6m+3,then the restrictive conditions of the latter are less than the other one.

关 键 词：泛对角线幻方 偏差分均匀矩阵 有心偏差分均匀矩阵 3等分偏差分均匀矩阵 泛对角线拉丁方 数集 奇数阶幻方 

分 类 号：O151.21[理学—数学]