Conjugate Orthogonal Diagonal Latin Squares with Missing Subsquares
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.
KeywordsStein Tral Dene
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