构造奇数阶超级幻方的两种方法

Two Approaches to Establish Ultra-Magic Squares of Odd Order

幻方是组合数学区组设计研究的一个新领域,与正交拉丁方存在天然联系。构造奇数阶超级幻方具有诸多约束条件,引起研究者兴趣。分别利用两个正交奇数阶超级拉丁方和中国象棋马步及兵步结合的排序方式,给出了两种构造奇数阶超级幻方的方法。在文末给出5,7,9阶超级幻方的例。

Magic square is a new field of combinatorial block design, which has a natural relationship with orthogonal Latin square. The construction of odd order ultra-magic square has many constraints, which attracts the interest of researchers. Using two orthogonal odd order ultra-Latin squares and the combination of the Chinese chess horse and pawn steps, led to two methods of constructing odd order ultra-magic squares. At the end of the paper, we give examples of ultra-magic square of order 5, 7, 9.