The Existence of Latin Squares without Orthogonal Mates
A latin square is a bachelor square if it does not possess an
orthogonal mate; equivalently, it does not have a decomposition into
disjoint transversals. We define a latin square to be a confirmed
bachelor square if it contains an entry through which there is no
transversal. We prove the existence of confirmed bachelor squares for
all orders greater than three. This resolves the existence question
for bachelor squares.
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Last modified: Mon May 19 16:45:27 EST 2006