“School of Mathematics”
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| Paper IPM / M / 7294 |
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| Abstract: | |
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In 1990, Kolesova, Lam and Thiel determined the 283,657 main
classes of Latin squares of order 8. Using techniques to determine
relevant Latin trades and integer programming, we examine
representatives of each of these main classes and determine that
none can contain a uniquely completable set of size less than 16.
In three of these main classes, the use of trades which contain
less than or equal to three rows, columns, or entries does not
suffice to determine this fact. We closely examine properties of
representatives of these three main classes. Writing the main
result in Nelder's notation for critical sets, we prove that
scs(8)=16.
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