Searching for Doubly Self-orthogonal Latin Squares

  • Runming Lu
  • Sheng Liu
  • Jian Zhang
Conference paper

DOI: 10.1007/978-3-642-23786-7_41

Volume 6876 of the book series Lecture Notes in Computer Science (LNCS)
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

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).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Runming Lu
    • 1
    • 2
  • Sheng Liu
    • 1
    • 2
  • Jian Zhang
    • 1
  1. 1.State Key Laboratory of Computer ScienceInstitute of Software, Chinese Academy of SciencesChina
  2. 2.Graduate University, Chinese Academy of SciencesChina