The Non-existence of (3,1,2)-Conjugate Orthogonal Idempotent Latin Square of Order 10

  • Olivier Dubois
  • Gilles Dequen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2239)


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).


Search Space Binary Operation Automate Reasoning Multiplication Table Resolution Strategy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Olivier Dubois
    • 1
  • Gilles Dequen
    • 2
  1. 1.LIP6, CNRS-Université Paris 6Paris cedex 05France
  2. 2.LaRIA, Université de Picardie Jules Verne CURIAmiensFrance

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