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On d-row (Column) Antimagic Matrices and Subset Partitions
Acta Mathematicae Applicatae Sinica, English Series ( IF 0.9 ) Pub Date : 2021-01-01 , DOI: 10.1007/s10255-021-0990-3
Zhi-he Liang , Shi-xin Liang

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。
更新日期:2021-01-01
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