Constructing All Magic Squares of Order Three

2004/09/24 by Guoce Xin, Xin, Guoce
Computer Science · Mathematics · #05A15 #11P21 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Number Theory (math.NT) #math.CO #math.NT #msc:05A15 #msc:11P21

paper · pdf · doi:10.48550/arxiv.math/0409468

7 pages

arxiv created 2004/09/24 · openalex publication_date 2004/09/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We find by applying MacMahon's partition analysis that all magic squares of order three, up to rotations and reflections, are of two types, each generated by three basis elements. A combinatorial proof of this fact is given.

Citations

• Algebraic Combinatorics of Magic Squares

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