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On d-row (Column) Antimagic Matrices and Subset Partitions

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Abstract

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].

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Authors and Affiliations

  1. School of Mathematical Science, Hebei Normal University, Shijiazhuang, 050024, China

    Zhi-he Liang

  2. ABB Electric Transmission Systems Co. LTD, Beijing, 100020, China

    Shi-xin Liang

Authors
  1. Zhi-he Liang
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  2. Shi-xin Liang
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Corresponding author

Correspondence to Zhi-he Liang.

Additional information

This paper is supported by the National Natural Science Foundation of China (No. 11871190).

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Liang, Zh., Liang, Sx. On d-row (Column) Antimagic Matrices and Subset Partitions. Acta Math. Appl. Sin. Engl. Ser. 37, 192–200 (2021). https://doi.org/10.1007/s10255-021-0990-3

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  • DOI: https://doi.org/10.1007/s10255-021-0990-3

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