References
[1]. Betsch, G. (2005) “Adventures in group theory: Rubik ’s Cube, Merlin ’s Machine & Other Mathematical Toys,” The Mathematical Intelligencer, 27(2), pp. 92–92. Available at: https://doi.org/10.1007/bf02985810.
[2]. Cornock, C. (2015) “Teaching group theory using Rubik's Cubes,” International Journal of Mathematical Education in Science and Technology, 46(7), pp. 957–967. Available at: https://doi.org/10.1080/0020739x.2015.1070442.
[3]. Holt, D.F., Eick, B. and O'Brien, E.A. (2020) Handbook of Computational Group theory. S.l.: CRC PRESS.
[4]. “Introduction to group theory” (2010) Symmetries and Conservation Laws in Particle Physics, pp. 25–46. Available at: https://doi.org/10.1142/9781848167049_0002.
[5]. “Permutation groups: A complexity overview” (2003) Permutation Group Algorithms, pp. 48–54. Available at: https://doi.org/10.1017/cbo9780511546549.003.
[6]. Atkinson, M.D. (1975) “An algorithm for finding the blocks of a permutation group,” Mathematics of Computation, 29(131), pp. 911–913. Available at: https://doi.org/10.1090/s0025-5718-1975-0367030-3.
[7]. Okamoto, A. (no date) “Group theory visualized through the Rubik’s Cube.” Available at: https://doi.org/10.15760/honors.1001.
[8]. Chen, J. J. (2004). Group theory and the Rubik’s cube.
[9]. Cornell, C. (2018) Rubik's cube: How to solve a Rubik's Cube including Rubik's Cube algorithms. United States.
[10]. El-Sourani, N., Hauke, S. and Borschbach, M. (2010) “An evolutionary approach for solving the Rubik’s cube incorporating exact methods,” Applications of Evolutionary Computation, pp. 80–89. Available at: https://doi.org/10.1007/978-3-642-12239-2_9.
Cite this article
Yu,J.;Li,W. (2023). The Rubik’s Cubes in Group Theory. Theoretical and Natural Science,5,275-281.
Data availability
The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.
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References
[1]. Betsch, G. (2005) “Adventures in group theory: Rubik ’s Cube, Merlin ’s Machine & Other Mathematical Toys,” The Mathematical Intelligencer, 27(2), pp. 92–92. Available at: https://doi.org/10.1007/bf02985810.
[2]. Cornock, C. (2015) “Teaching group theory using Rubik's Cubes,” International Journal of Mathematical Education in Science and Technology, 46(7), pp. 957–967. Available at: https://doi.org/10.1080/0020739x.2015.1070442.
[3]. Holt, D.F., Eick, B. and O'Brien, E.A. (2020) Handbook of Computational Group theory. S.l.: CRC PRESS.
[4]. “Introduction to group theory” (2010) Symmetries and Conservation Laws in Particle Physics, pp. 25–46. Available at: https://doi.org/10.1142/9781848167049_0002.
[5]. “Permutation groups: A complexity overview” (2003) Permutation Group Algorithms, pp. 48–54. Available at: https://doi.org/10.1017/cbo9780511546549.003.
[6]. Atkinson, M.D. (1975) “An algorithm for finding the blocks of a permutation group,” Mathematics of Computation, 29(131), pp. 911–913. Available at: https://doi.org/10.1090/s0025-5718-1975-0367030-3.
[7]. Okamoto, A. (no date) “Group theory visualized through the Rubik’s Cube.” Available at: https://doi.org/10.15760/honors.1001.
[8]. Chen, J. J. (2004). Group theory and the Rubik’s cube.
[9]. Cornell, C. (2018) Rubik's cube: How to solve a Rubik's Cube including Rubik's Cube algorithms. United States.
[10]. El-Sourani, N., Hauke, S. and Borschbach, M. (2010) “An evolutionary approach for solving the Rubik’s cube incorporating exact methods,” Applications of Evolutionary Computation, pp. 80–89. Available at: https://doi.org/10.1007/978-3-642-12239-2_9.