Abstract
To denote a (3,1,2)-conjugate orthogonal idempotent latin square of order n, the usual acronym is (3,1,2)-COILS(n). Up to now, existence of a (3,1,2)-COILS(n) had been proved for every positive integer n except n = 2, 3, 4, 6, for which the problem was answered in the negative, and n = 10, for which it remained open. In this paper, we use a computer program to prove that a (3,1,2)-COILS(10) does not exist. Following along the lines of recent studies which led to the solution, by means of computer programs, of many open latin square problems, we use a constraint satisfaction technique combining an economical representation of (3,1,2)-COILS with a drastic reduction of the search space. In this way, resolution time is improved by a ratio of 104, as compared with current computer programs. Thanks to this improvement in performance, we are able to prove the non-existence of a (3,1,2)-COILS(10).
This work was supported by Advanced Micro Devices Inc.
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Dubois, O., Dequen, G. (2001). The Non-existence of (3,1,2)-Conjugate Orthogonal Idempotent Latin Square of Order 10. In: Walsh, T. (eds) Principles and Practice of Constraint Programming — CP 2001. CP 2001. Lecture Notes in Computer Science, vol 2239. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45578-7_8
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DOI: https://doi.org/10.1007/3-540-45578-7_8
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