Conjugate Orthogonal Diagonal Latin Squares with Missing Subsquares

  • Frank E. Bennett
  • Beiliang Du
  • Hantao Zhang
Part of the Mathematics and Its Applications book series (MAIA, volume 563)


We shall refer to a diagonal Latin square which is orthogonal to its (3, 2, 1)-conjugate, and the latter is also a diagonal Latin square, as a (3, 2, 1)-conjugate orthogonal diagonal Latin square, briefly CODLS. This article investigates the spectrum of CODLS with a missing sub-square. The main purpose of this paper is two-fold. First of all, we show that for any positive integers n ≥ 1, a CODLS of order υ with a missing subsquare of order n exists if υ ≥ 13n/4 + 93 and υ - n is even. Secondly, we show that for 2 ≤ n ≤ 6, a CODLS of order υ with a missing subsquare of order n exists if and only if υ ≥ 3n + 2 and υ - n is even, with one possible exception.


Positive Integer Disjoint Subset Parallel Class Multiplication Table Steiner Triple System 
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Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Frank E. Bennett
    • 1
  • Beiliang Du
    • 2
  • Hantao Zhang
    • 3
  1. 1.Department of MathematicsMount Saint Vincent UniversityHalifaxCanada
  2. 2.Department of MathematicsSuzhou UniversitySuzhouP.R.China
  3. 3.Computer Science DepartmentThe University of IowaIowa CityUSA

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