Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30184
The Game of Synchronized Quadromineering

Authors: Alessandro Cincotti

Abstract:

In synchronized games players make their moves simultaneously rather than alternately. Synchronized Quadromineering is the synchronized version of Quadromineering, a variants of a classical two-player combinatorial game called Domineering. Experimental results for small m × n boards (with m + n < 15) and some theoretical results for general k × n boards (with k = 4, 5, 6) are presented. Moreover, some Synchronized Quadromineering variants are also investigated.

Keywords: Combinatorial games, Synchronized games, Quadromineering.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1079554

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 881

References:


[1] E. R. Berlekamp, "Blockbusting and Domineering," Journal of Combinatorial Theory Ser. A, vol. 49, pp. 67-116, 1988.
[2] E. R. Berlekamp, J. H. Conway, R. K. Guy, Winning way for your mathematical plays, A K Peters, 2001.
[3] S. A. Blanco, A. S. Fraenkel, "Triomineering, Tridomineering, and L-Tridomineering," Technical Report MCS04- 10, Department of Computer Science and Applied Mathematics, The Weizmann Institute of Science. Available: http://wisdomarchive.wisdom.weizmann.ac.il:81/ archive/00000367/.
[4] D. M. Breuker, J. W. H. M. Uiterwijk, H. J. van den Herik, "Solving 8 × 8 Domineering," Theoretical Computer Science, vol. 230, pp. 195-206, 2000.
[5] N. Bullock, "Domineering: Solving Large Combinatorial Search Space," ICGA Journal, vol. 25, no. 2, pp. 67-84, 2002.
[6] A. Cincotti, H. Iida, "The Game of Synchronized Cutcake," in Proc. of the IEEE Symposium on Computational Intelligence and Games, Honolulu, 2007, pp. 374-379.
[7] A. Cincotti, H. Iida, "The Game of Synchronized Maundy Cake," in Proc. of the 7th Annual Hawaii International Conference on Statistics, Mathematics and Related Fields, Honolulu, 2008, pp. 422-429.
[8] A. Cincotti, H. Iida, "The Game of Synchronized Domineering," in Proc. of the Conference on Computers and Games 2008, Beijing, 2008, pp. 241-251.
[9] A. Cincotti, S. Komori, H. Iida, "The game of Synchronized Triomineering and Synchronized Tridomineering," International Journal of Computational and Mathematical Sciences, vol. 2, pp. 143-148, 2008.
[10] J. H. Conway, On Numbers and Games, A K Peters, 2001.
[11] M. Gardner, "Mathematical games," Scientific American vol. 230, pp. 106-108, 1974.
[12] M. Lachmann, C. Moore, I. Rapaport, "Who Wins Domineering on Rectangular Boards," in R. J. Nowakowski (ed.) More Games of No Chance, vol. 42, pp. 307-315, Cambridge University Press 2002.