Linear Type-p Most-Perfect Squares

2017/12/27 by John Lorch, Lorch, John
Mathematics · #05B30 #05B33 #Advanced Optimization Algorithms Research #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05B30 #msc:05B33

paper · pdf · doi:10.48550/arxiv.1712.09600

10 pages

arxiv created 2017/12/27 · openalex publication_date 2017/12/27 · arxiv updated 2017/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe a generalization of most-perfect magic squares, called type-p most-perfect squares, and in prime-power orders we give a linear construction of these squares reminiscent of de la Loubere's classical magic square construction method. Type-p most-perfect squares can be used to construct other interesting squares (e.g., generalized Franklin squares) and our linear construction may have implications for counting type-p most-perfect squares.

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