1. ON THE SPECTRUM OF r-ORTHOGONAL LATIN SQUARES OF DIFFERENT ORDERS.
- Author
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AMJADI, H., SOLTANKHAH, N., SHAJARISALES, N., and TAHVILIAN, M.
- Subjects
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MAGIC squares , *NUMBER theory , *ROTAS-Sator square , *ORTHOGONALIZATION , *MATHEMATICS - Abstract
Two Latin squares of order n are orthogonal if in their superposition, each of the n2 ordered pairs of symbols occurs exactly once. Colbourn, Zhang and Zhu, in a series of papers, determined the integers r for which there exist a pair of Latin squares of order n having exactly r different ordered pairs in their superposition. Dukes and Howell defined the same problem for Latin squares of different orders n and n+k. They obtained a non-trivial lower bound for r and solved the problem for k ≥2n/3 . Here for k < 2n/3 , some constructions are shown to realize many values of r and for small cases (3 ≤ n ≤ 6), the problem has been solved. [ABSTRACT FROM AUTHOR]
- Published
- 2016