2020/08/23 by P. D. Loly, Peter D. Loly, Ian Cameron +3 · 1 citation
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #History and Overview (math.HO) #Number Theory (math.NT) #graph theory and CDMA systems #math.CO #math.HO #math.NT
paper · pdf · doi:10.48550/arxiv.2008.11020
31 pages
openalex publication_date 2020/08/23 · arxiv created 2020/09/16 · arxiv updated 2020/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Frierson used a powerful parameterization of the pattern of the order 3 associative magic square to construct a family of six related order 9 compound (or composite) magic squares, several of them ancient. Stimulated by Bellew's 1997 extension to order 27, we extend these ideas to all orders that are powers of 3, and in addition find simple formulae for the matrix spectra and entropic measures for all those orders. This construction is fractal and we give numerical results to order 243 which show an information entropy measure converging to a constant value of about 1.168.. for the lowest entropy members. We also briefly consider compounding of an order 4 magic square with the lowest entropy, for which we find a similar trend to constant entropy.