On a conjecture by Sylwia Cichacz and Tomasz Hinc, and a related problem
Fiorenza Morini, Marco Antonio Pellegrini, Stefania Sora · Discrete Applied Mathematics · 2025
A Γ -magic rectangle set MRS Γ ( a , b ; c ) is a collection of c arrays of size a × b whose entries are the elements of an abelian group Γ of order a b c , each one appearing once and in a unique array in such a way that the sum of the entries of each row is equal to a constant ω ∈ Γ and the sum of the entries of each column is equal to a constant δ ∈ Γ . 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 MRS Γ ( a , b ; c ) . We also generalize this problem describing constructions of Γ -magic rectangle sets whose elements are partially filled arrays.