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Conjugate Orthogonal Diagonal Latin Squares with Missing Subsquares

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

Abstract

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.

Keywords

Positive Integer Disjoint Subset Parallel Class Multiplication Table Steiner Triple System 
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 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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