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.
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References
Cavenagh N.J.: Avoidable partial Latin squares of order 4m + 1. Ars Combin. 95, 257–275 (2010)
Chetwynd A.G., Rhodes S.J.: Chessboard squares. Discrete Math. 141(1-3), 47–59 (1995)
Chetwynd A.G., Rhodes S.J.: Avoiding partial Latin squares and intricacy. Discrete Math. 177(1-3), 17–32 (1997)
Häggkvist R.: A note on Latin squares with restricted support. Discrete Math. 75(1-3), 253–254 (1989)
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Öhman, LD. Partial Latin Squares Are Avoidable. Ann. Comb. 15, 485–497 (2011). https://doi.org/10.1007/s00026-011-0106-5
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DOI: https://doi.org/10.1007/s00026-011-0106-5