Abstract
Two orthogonal latin squares of order n have the property that when they are superimposed, each of the n 2 ordered pairs of symbols occurs exactly once. In a series of papers, Colbourn, Zhu, and Zhang completely determine the integers r for which there exist a pair of latin squares of order n having exactly r different ordered pairs between them. Here, the same problem is considered for latin squares of different orders n and m. A nontrivial lower bound on r is obtained, and some embedding-based constructions are shown to realize many values of r.
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Research supported in part by NSERC.
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Dukes, P., Howell, J. The Orthogonality Spectrum for Latin Squares of Different Orders. Graphs and Combinatorics 29, 71–78 (2013). https://doi.org/10.1007/s00373-011-1092-4
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DOI: https://doi.org/10.1007/s00373-011-1092-4