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

• Autorzy: Ziqi Lin , Sijie Liu , Kai-Tai Fang , Yuhui Deng
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Magic square of order 5; Basic form; Generating vectors; Frénicle-Amela patterns

• Wydawca: De Gruyter Open
• Czasopismo: Special Matrices
• Rocznik: 2016
• Tom: 4
• Numer: 1
• Strony: 110-120

Daty

otrzymano

2015-10-19

zaakceptowano

2016-01-12

online

2016-02-02

Twórcy

autor

Ziqi Lin

• Division of Science and Technology, BNU-HKBU United International College, Zhuhai, China

autor

Sijie Liu

• Division of Science and Technology, BNU-HKBU United International College, Zhuhai, China

autor

Kai-Tai Fang

• Division of Science and Technology, BNU-HKBU United International College, Zhuhai, China

autor

Yuhui Deng

• Division of Science and Technology, BNU-HKBU United International College, Zhuhai, China

Bibliografia

• [1] Candy, A. L., 1937: Construction, Classification and Census of Magic Squares of Order 5. Edwards brothers, 249 pp.
• [2] Chinese Magic Square, 2014: Accessed 12 June 2014.
• [Available online at http://www.zhghf.net/.]
• [3] Clifford, A. P., 2003: The Zen of Magic Squares, Circles, and Stars. Princeton University Press, 373 pp.
• [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.
• [5] Garder, M., 1975: Mathematical games, A breakthrough in magic squares, and the first perfect magic cube. Scientific American, 118-123.
• [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.
• [7] Schroeppel, R., 1976: The Order 5 Magic Squares Program, Scientific American.
• [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.
• [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.]
• [10] Baidu Tieba, 2010: Accessed 11 June 2014. [Available online at http://tieba.baidu.com/p/957776994?pid=10675158083& cid=0&from=prin\sharp10675158083?from=prin.]

Identyfikatory

DOI

10.1515/spma-2016-0011