Abstract
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).
This work is partially supported by the National Natural Science Foundation of China (NSFC) under grant No. 60673044. Corresponding author: Jian Zhang. We are grateful to the anonymous reviewers for their comments, to Lie Zhu and Feifei Ma for their help in this research.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Du, B., Zhu, L.: Existence of doubly self-orthogonal Latin squares. Bulletin of the Institute of Combinatorics and its Applications (Bulletin of the ICA) 20, 13–18 (1997)
Dubois, O., Dequen, G.: The non-existence of (3, 1, 2)-conjugate orthogonal idempotent Latin square of order 10. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 108–120. Springer, Heidelberg (2001)
Heinrich, K., Hilton, A.J.W.: Doubly diagonal orthogonal latin squares. Discrete Mathematics 46(2), 173–182 (1983)
Kim, K., Prasanna-Kumar, V.K.: Perfect Latin squares and parallel array access. SIGARCH Comput. Archit. News 17(3), 372–379 (1989)
Knuth, D.E.: Dancing links. Arxiv preprint cs/0011047 (2000)
Östergård, P.R.J.: Constructing combinatorial objects via cliques. In: Webb, B.S. (ed.) Surveys in Combinatorics. London Mathematical Society Lecture Note Series, vol. 327, pp. 57–82. Cambridge University Press, Cambridge (2005)
Vasquez, M.: New results on the queens_n \(^{\mbox{2}}\) graph coloring problem. J. of Heuristics 10(4), 407–413 (2004)
Zhang, H.: Combinatorial designs by SAT solvers. In: Biere, A., Heule, M., van Maaren, H., Walsh, T. (eds.) Handbook of Satisfiability, vol. 2. IOS Press, Amsterdam (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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. https://doi.org/10.1007/978-3-642-23786-7_41
Download citation
DOI: https://doi.org/10.1007/978-3-642-23786-7_41
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23785-0
Online ISBN: 978-3-642-23786-7
eBook Packages: Computer ScienceComputer Science (R0)