On the Distances between Latin Squares and the Smallest Defining Set Size |
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| Authors: | Nicholas Cavenagh Reshma Ramadurai |
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| Institution: | Department of Mathematics, The University of Waikato, Hamilton, New Zealand |
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| Abstract: | In this note, we show that for each Latin square L of order  , there exists a Latin square  of order n such that L and  differ in at most  cells. Equivalently, each Latin square of order n contains a Latin trade of size at most  . We also show that the size of the smallest defining set in a Latin square is  . |
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| Keywords: | Latin square Latin trade defining set critical set Hamming distance |
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, there exists a Latin square 
of order n such that L and 
differ in at most 
cells. Equivalently, each Latin square of order n contains a Latin trade of size at most 
. We also show that the size of the smallest defining set in a Latin square is 
.