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Some results on magic squares based on generating magic vectors and R-C similar transformations

Xiaoyang Ma;  Kai-tai Fang;  Yu hui Deng — 2017

Special Matrices

In this paper we propose a new method, based on R-C similar transformation method, to study classification for the magic squares of order 5. The R-C similar transformation is defined by exchanging two rows and related two columns of a magic square. Many new results for classification of the magic squares of order 5 are obtained by the R-C similar transformation method. Relationships between basic forms and R-C similar magic squares are discussed. We also propose a so called GMV (generating magic...

Generation of all magic squares of order 5 and interesting patterns finding

Ziqi Lin;  Sijie Liu;  Kai-Tai Fang;  Yuhui Deng — 2016

Special Matrices

This paper presents an enumeration algorithm to generate all magic squares of order 5 based on the ideas of basic form (Schroeppel [7]) and generating vector which is extension of Frénicle Quads (Ollerenshaw and Bondi [6]). The results lead us to extend Frénicle-Amela patterns from the case of order 4 to the case of order 5, which we refer to Frénicle-Amela-Like patterns. We show that these interesting Frénicle-Amela-Like patterns appear simultaneously. The number of these patterns is also calculated....

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