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

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

Special Matrices (2016)

  • Volume: 4, Issue: 1, page 110-120
  • ISSN: 2300-7451

Abstract

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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.

How to cite

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Ziqi Lin, et al. "Generation of all magic squares of order 5 and interesting patterns finding." Special Matrices 4.1 (2016): 110-120. <http://eudml.org/doc/276658>.

@article{ZiqiLin2016,
abstract = {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.},
author = {Ziqi Lin, Sijie Liu, Kai-Tai Fang, Yuhui Deng},
journal = {Special Matrices},
keywords = {Magic square of order 5; Basic form; Generating vectors; Frénicle-Amela patterns; magic square of order 5; basic form; generating vectors; Frénicle-Amela patterns},
language = {eng},
number = {1},
pages = {110-120},
title = {Generation of all magic squares of order 5 and interesting patterns finding},
url = {http://eudml.org/doc/276658},
volume = {4},
year = {2016},
}

TY - JOUR
AU - Ziqi Lin
AU - Sijie Liu
AU - Kai-Tai Fang
AU - Yuhui Deng
TI - Generation of all magic squares of order 5 and interesting patterns finding
JO - Special Matrices
PY - 2016
VL - 4
IS - 1
SP - 110
EP - 120
AB - 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.
LA - eng
KW - Magic square of order 5; Basic form; Generating vectors; Frénicle-Amela patterns; magic square of order 5; basic form; generating vectors; Frénicle-Amela patterns
UR - http://eudml.org/doc/276658
ER -

References

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  1. [1] Candy, A. L., 1937: Construction, Classification and Census of Magic Squares of Order 5. Edwards brothers, 249 pp.  Zbl64.0989.06
  2. [2] Chinese Magic Square, 2014: Accessed 12 June 2014.  
  3. [Available online at http://www.zhghf.net/.]  
  4. [3] Clifford, A. P., 2003: The Zen of Magic Squares, Circles, and Stars. Princeton University Press, 373 pp.  
  5. [4] Fang, K. T., Luo, Y. Y., and Zheng, Y. X., 2015: Classification of magic squares of order 4. Proc. IWMS. Haikou, China, International Workshop on Matrices and Statistics, 84-97.  
  6. [5] Garder, M., 1975: Mathematical games, A breakthrough in magic squares, and the first perfect magic cube. Scientific American, 118-123.  
  7. [6] Ollerenshaw, K., and Bondi, H., 1982:Magic squares of order four. Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 306, 443-532.  Zbl0492.05022
  8. [7] Schroeppel, R., 1976: The Order 5 Magic Squares Program, Scientific American.  
  9. [8] Styan, G. P. H., 2014: Some illustrated comments on 5 x 5 goldenmagicmatrices and on 5 x 5 Stifelsche Quadrate. 23rd Conf. International Workshop on Matrices and Statistics, Ljubljana, Slovenia, 41 pp.  
  10. [9] Trump, W., 2012: How many magic squares are there? Accessed 12 June 2014. [Available online at http://www.trump.de/ magic-squares/howmany.html.]  
  11. [10] Baidu Tieba, 2010: Accessed 11 June 2014. [Available online at http://tieba.baidu.com/p/957776994?pid=10675158083 cid=0from=prin♯10675158083?from=prin.] 

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