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2016 | 4 | 1 | 110-120
Tytuł artykułu

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

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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.
Wydawca
Czasopismo
Rocznik
Tom
4
Numer
1
Strony
110-120
Opis fizyczny
Daty
otrzymano
2015-10-19
zaakceptowano
2016-01-12
online
2016-02-02
Twórcy
autor
  • Division of Science and Technology, BNU-HKBU United International College, Zhuhai, China
autor
  • Division of Science and Technology, BNU-HKBU United International College, Zhuhai, China
autor
  • Division of Science and Technology, BNU-HKBU United International College, Zhuhai, China
autor
  • 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.]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_spma-2016-0011
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