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

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 sq...

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Bibliographic Details
Published in:Special matrices 2017-01, Vol.5 (1), p.82-96
Main Authors: Ma, Xiaoyang, Fang, Kai-tai, Deng, Yu hui
Format: Article
Language:English
Subjects:
Generating magic vector
Magic squares
Similar matrix
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Summary: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 vector) class set method for classification of magic squares of order 5, presenting 42 categories in total.
ISSN:2300-7451
2300-7451
DOI:10.1515/spma-2017-0009