On the distances between Latin squares and the smallest defining set size
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This is an author’s accepted version of an article published in the journal: Electronic Notes in Discrete Mathematics. © 2016 Elsevier B.V.
Abstract
We show that for each Latin square L of order n ≥ 2 , there exists a Latin square L’ ≠ L of order n such that L and L’ differ in at most 8√n̅ cells. Equivalently, each Latin square of order n contains a Latin trade of size at most 8√n̅ . We also show that the size of the smallest defining set in a Latin square is Ω(n³/²).
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Cavenagh, N. J., & Ramadurai, R. (2016). On the distances between Latin squares and the smallest defining set size. Electronic Notes in Discrete Mathematics, 54, 15–20. https://doi.org/10.1016/j.endm.2016.09.004
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Elsevier