Searching for Doubly Self-orthogonal Latin Squares
- Cite this paper as:
- Lu R., Liu S., Zhang J. (2011) Searching for Doubly Self-orthogonal Latin Squares. In: Lee J. (eds) Principles and Practice of Constraint Programming – CP 2011. CP 2011. Lecture Notes in Computer Science, vol 6876. Springer, Berlin, Heidelberg
A Doubly Self Orthogonal Latin Square (DSOLS) is a Latin square which is orthogonal to its transpose to the diagonal and its transpose to the back diagonal. It is challenging to find a non-trivial DSOLS. For the orders n = 2 (mod 4), the existence of DSOLS(n) is unknown except for n = 2, 6. We propose an efficient approach and data structure based on a set system and exact cover, with which we obtained a new result, i.e., the non-existence of DSOLS(10).
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