The Spectrum of R-Orthogonal Latin Squares

  • Charles J. Colbourn
  • L. Zhu
Part of the Mathematics and Its Applications book series (MAIA, volume 329)


Two latin squares of side n are r-orthogonal if, when superimposed, there are exactly r distinct ordered pairs. In this paper, it is established that for all n ≥ 27, r-orthogonal latin squares of side n exist if and only if n + 2 ≤ rn 2 — 2 or r ∊ {n, n 2}. An almost complete solution is given for smaller sides.


Small Side Balance Incomplete Block Design Group Divisible Design Column Permutation Auxiliary Notion 
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Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Charles J. Colbourn
    • 1
  • L. Zhu
    • 1
    • 2
  1. 1.Combinatorics and OptimizationUniversity of WaterlooWaterlooCanada
  2. 2.Department of MathematicsSuzhou UniversitySuzhouChina

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