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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.23662 |
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| _version_ | 1866909617707024384 |
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| author | Yu, Shikang Feng, Tao Liu, Hengrui |
| author_facet | Yu, Shikang Feng, Tao Liu, Hengrui |
| contents | 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 $γ\in G$ and the sum of each column in every array equals a constant $δ\in G$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_23662 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence of magic rectangle sets over finite abelian groups Yu, Shikang Feng, Tao Liu, Hengrui Combinatorics 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 $γ\in G$ and the sum of each column in every array equals a constant $δ\in G$. 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. |
| title | Existence of magic rectangle sets over finite abelian groups |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2410.23662 |