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arXiv · 2410.23662

Existence of magic rectangle sets over finite abelian groups

Shikang Yu·Tao Feng·Hengrui Liu
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Abstract

Let $a$, $b$ and $c$ be positive integers. Let $(G,+)$ be a finite abelian group of order $abc$. A $G$-magic rectangle set MRS$_G(a,b;c)$ is a collection of $c$ arrays of size $a\times b$ whose entries are elements of a group $G$, each appearing exactly once, such that the sum of each row in every array equals a constant $\gamma\in G$ and the sum of each column in every array equals a constant $\delta\in G$. This paper establishes the necessary and sufficient conditions for the existence of an MRS$_G(a,b;c)$ for any finite abelian group $G$, thereby confirming a conjecture presented by Cichacz and Hinc.

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Shikang Yu, Tao Feng, Hengrui Liu. 2024-10-31. Existence of magic rectangle sets over finite abelian groups. https://doi.org/10.1002/jcd.21987

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