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The Spectrum of R-Orthogonal Latin Squares

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

Abstract

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.

Keywords

Small Side Balance Incomplete Block Design Group Divisible Design Column Permutation Auxiliary Notion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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