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Constructing Pandiagonal Snowflake Magic Squares of Odd Order 被引量:3
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作者 ZHANGShi-de HUQing-wen WANGJi-zhao 《Chinese Quarterly Journal of Mathematics》 CSCD 2004年第2期172-185,共14页
The constructional methods of pandiagonal snowflake magic squares of orders 4m are established in paper [3]. In this paper, the constructional methods of pandiagonal snowflake magic squares of odd orders n are establi... The constructional methods of pandiagonal snowflake magic squares of orders 4m are established in paper [3]. In this paper, the constructional methods of pandiagonal snowflake magic squares of odd orders n are established with n = 6m+l, 6m+5 and 6m+3, m is an odd positive integer and m is an even positive integer 9|6m + 3. It is seen that the number sets for constructing pandiagonal snowflake magic squares can be extended to the matrices with symmetric partial difference in each direction for orders 6m + 1 , 6m + 5; to the trisection matrices with symmetric partial difference in each direction for order 6m + 3. 展开更多
关键词 pandiagonal magic squares matrix with uniform partial difference in each direction matrix with symmetric partial difference in each direction trisection matrix with uniform partial difference in each direction semi-pandiagonal Latin square
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奇数阶幻方、泛对角线幻方构作数集的拓广
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作者 张世德 王俊卿 朱红莺 《河南师范大学学报(自然科学版)》 CAS CSCD 2001年第2期9-15,共7页
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... 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 。 展开更多
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
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