An m × k matrix is said to be a d -row (column) antimagic matrix if its row-sums (column-sums) form an arithmetic progression with a difference d . The goal of this paper is to obtain the existence theorems and construction methods of some d -row (column) antimagic matrices. Using these results we give the necessary and sufficient condition for the existence of an ( m, d )-partition of [1, mk ].

中文翻译：

---

在 d 行（列）反幻矩阵和子集分区上

如果 m × k 矩阵的行总和（列总和）形成一个差为 d 的等差数列，则称该矩阵为 ad 行（列）反幻矩阵。本文的目标是获得一些d行（列）反幻矩阵的存在定理和构造方法。使用这些结果，我们给出了 [1, mk ] 的 ( m, d )-分区存在的充分必要条件。