Work

Existence of Magic Rectangle Sets Over Finite Abelian Groups

Year: 2025

Type: article

Abstract: ABSTRACT Let , and be positive integers. Let be a finite abelian group of order . A ‐magic rectangle set is a collection of arrays of size , whose entries are elements of a group , each appearing exactly once, such that the sum of each row in every array equals a constant , and the sum of each column in every array equals a constant . This paper establishes the necessary and sufficient conditions for the existence of an , for any finite abelian group , thereby confirming a conjecture posted by Cichacz and Hinc.

Source: Journal of Combinatorial Designs

DOI: 10.1002/jcd.21987

Authors: Shikang Yu, Tao Feng, Hengrui Liu

Institution: Beijing Jiaotong University

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

Award: G4089320920