- 會議論文
Numerical Enumeration of Greco-Latin Prime Order Associative Magic Squares
並列摘要
A magic square of order n consists of the numbers 1 to n^2 placed such that the sum of each row, column and principal diagonal equals the magic sum n(n^2 +1)/2. In addition, an odd ordered magic square is associative or self-complementary if diagonally opposite elements have the same sum (n^2 +1)/2. The magic square is said to be regular Greco-Latin if it can be decomposed as a sum of a pair of Latin squares. Here, a numerical construction of associative magic squares based on Bree's Orthogonality Criterion is presented. This construction method replicates the known algorithms, e.g., the Siamese method and the Pyramid method. Duplications are identified, and this leads to a count of the unique regular Greco-Latin associative magic squares of prime order.
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延伸閱讀
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