On a conjecture by Sylwia Cichacz and Tomasz Hinc, and a related problem

2024/08/09 by Morini, Fiorenza, Pellegrini, Marco Antonio, Sora, Stefania
#05B15 #05B30 #05C78 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2408.04897

Abstract

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 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 ω∈ Γ and the sum of the elements 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.

Related

• Existence of magic rectangle sets over finite abelian groups
• Magic partially filled arrays on abelian groups
• Magic rectangles with empty cells
• Magic squares on Abelian groups
• Signed magic rectangles with three filled cells in each column