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Partial Latin Squares Are Avoidable
Lars-Daniel Öhman
Department of Mathematics and Mathematical Statistics, Umeå University, SE-90187 Umeå, Sweden
lars-daniel.ohman@math.umu.se
Annals of Combinatorics 15 (3) pp.485-497 July, 2011
AMS Subject Classification: 05B15
Abstract:
A square array is avoidable if for each set of n symbols there is an n×n Latin square on these symbols which differs from the array in every cell. The main result of this paper is that for m ≥ 2 any partial Latin square of order 4m−1 is avoidable, thus concluding the proof that any partial Latin square of order at least 4 is avoidable.
Keywords: Latin square, partial Latin square, avoidable array

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