幻方

用遗传算法构造n阶幻方

Constructing n-order Magic Square by Using Genetic Algorithm

2~n（n≥3）阶双重幻方的一种构造方法

A kind of constructive method to 2 ~ n ( n ≥ 3 ) order twofold magic square

n阶双重幻方的构造

The construction of twofold magic square of order n

用n阶半幻方造n~2阶泛对角线幻方

Constructing A Set of n ~ 2-orders Pandiagonal Magic Square by Using a N-orders Semi Magic Square

给出了构造3~n（n≥2）阶双重幻方的一种方法。

A constructive method about 3n ( n ≥ 2 ) order twofold magic squares is given .

给出了n＝sk时通过一个s×k辅助矩阵构造n阶泛对角幻方的方法。

New approach for constructing pandiagonal magic squares of order sk through s × k auxiliary arrays is provided .

本文给出一种从n阶自然方阵出发构造n~2阶全对称幻方的快速方法。

A method is given to construct an all - symmetric magic square of order n ~ 2 from a natural square matrix of order n.

用AB方和横纵换图造幻方

Use AB-Square and the Chart of Horizontal and Vertical Exchange to Make a Magic Square

在奇n阶幻方构造研究的基础上，发现了奇n阶幻立方和正交拉丁立方的构造方法。

On the base of magic squares constructions research of odd order a method of constructing magic cubes and mutually orthogonal latin cubes of odd order is discovered .

Franklin半幻方的一生多

Generating many Franklin Semi Magic Squares from One

在MATLAB上的实验结果表明，幻方变换全息图方法，生成一些类似数字全息图的图像，生成的图像彻底隐去原图的信息。

Experimental results based on MATLAB show that this approach can hide the information of the original image whole by generating some image patterns like FDCH .

提出并证明了：1.递归构造n阶幻方（n>4）的方法；

In this paper , the author gives some methods of constructing magic squares : 1 . a method of recursively constructing magic squares of order n ( n > 4 );

构造8k阶Franklin半幻方的又一公式

A New Formula of Constructing the 8k Orders Franklin Semi Magic Square

6m±1阶全对称幻方的一些构造方法

The Way of Making 6m-1 Order All-Symmetric Magic Square

4K阶强幻方构造法

A method of structuring strongly magic squares of 4 K orders

一类偶数（2n）阶幻方的基底构造法

Construction of even - order magic square

此算法对于研究其他类型的多重幻方以及其他NP难题，有着一定的参考价值。

This algorithm has a certain reference value for the study of other types of multi-magic squares and other NP problems .

构造任意4k阶保折和半幻方

Constructing Arbitrary 4k Orders Conserve Break Sum Semi Magic Square

4k阶幻方的对称交换构造法

Construction Method of Symmetric Swapping for the Magic Square of Order 4k

奇妙的Franklin半幻方造法揭秘及推广与调整

Revelation of the secret of the method of making the Franklin Half magic square and its extension and adjustment

用经列和纬行造8k阶Franklin半幻方

Constructing 8k Orders Franklin Semi Magic Square by Using Warp Column and Weft Row

4n阶完美幻方的新构造法

A new structuring method of perfect magic square of 4n orders

数集构成4n阶泛对角线幻方的充分条件

Sufficient condition of number set constructing pandiagonal magic square of order 4N

然而，多重幻方是一个典型的NP难题，利用计算机搜索幻方的时间复杂度是超乎人们想象的。

However , multi-magic square is a typical NP problem , time complexity that computer search a magic square are more than people think .

本文用C-程序实现行等和矩阵的构造，并利用行等和矩阵构造阶数为n（n≠4t+2,12t）的全对角线幻方。

A C-program composition method is given to construct pandiagonal magic square . In this paper we define row sum-equal matrix to construct pandiagonal magic square of order n ( n ≠ 4t + 2,12t ) .

通过对一类素数阶（N≥3）幻方算法的改进得到一类素数阶完全幻方的两种构造方法，并比较它们的特点。

This article aims at the improvement of the algorithm for a kind of exponent magic square of prime number , and gets two structual ways for a kind of complete exponent magic square of prime numbers .

本文给出构造4K阶强幻方的一般方法。

In this paper we give a method of structuring strongly magic Squares of 4k orders .

给出4n阶全对称幻方的一类构造方法，即先构造出n~2个第二类4阶等值全对称幻方砌块。

This paper presents a kind of method for constructing 4n-order all-symmetric magic square , i.

用6阶等值幻方砌块构成的6n阶幻方

6n-order magic square constructed by blocks of 6-order equivalent magic square

8t阶幻方及正交拉丁方的构造方法

Method of Constructing Magic Square and Mutually Orthogonal Latin Square of Order 8t