1. On a conjecture by Sylwia Cichacz and Tomasz Hinc, and a related problem
- Author
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Morini, Fiorenza, Pellegrini, Marco Antonio, and Sora, Stefania
- Subjects
Mathematics - Combinatorics ,05B15, 05C78, 05B30 - Abstract
A $\Gamma$-magic rectangle set $\mathrm{MRS}_\Gamma (a, b; c)$ is a collection of $c$ arrays of size $a\times b$ whose entries are the elements of an abelian group $\Gamma$ of order $abc$, each one appearing once and in a unique array in such a way that the sum of the elements of each row is equal to a constant $\omega \in \Gamma$ and the sum of the elements of each column is equal to a constant $\delta \in \Gamma$. In this paper we provide new evidences for the validity of a conjecture proposed by Sylwia Cichacz and Tomasz Hinc on the existence of an $\mathrm{MRS}_\Gamma(a,b;c)$. We also generalize this problem, describing constructions of $\Gamma$-magic rectangle sets, whose elements are partially filled arrays.
- Published
- 2024