The Game of Synchronized Triomineering and Synchronized Tridomineering

Authors: Alessandro Cincotti, Shigetaka Komori, Hiroyuki Iida

Abstract:

In synchronized games players make their moves simultaneously rather than alternately. Synchronized Triomineering and Synchronized Tridomineering are respectively the synchronized versions of Triomineering and Tridomineering, two variants of a classic two-player combinatorial game called Domineering. Experimental results for small m × n boards (with m + n ≤ 12 for Synchronized Triomineering and m + n ≤ 10 for Synchronized Tridomineering) and some theoretical results for general k×n boards (with k = 3, 4, 5 for Synchronized Triomineering and k = 3 for Synchronized Tridomineering) are presented. Future research is indicated.

Keywords: Combinatorial games, Synchronized games, Triomineering, Tridomineering.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1062916

References:

[1] 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/
[2] 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.
[3] 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.
[4] A. Cincotti, H. Iida, "The Game of Synchronized Domineering," in Proc. of the Conference on Computers and Games 2008, Beijing, 2008, pp. 241-251.