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Determinants of Latin squares of order 8. (English) Zbl 0876.05017
Summary: A Latin square is an $$n\times n$$ array of $$n$$ symbols in which each symbol appears exactly once in each row and column. Regarding each symbol as a variable and taking the determinant, we get a degree-$$n$$ polynomial in $$n$$ variables. Can two Latin squares $$L$$, $$M$$ have the same determinant, up to a renaming of the variables, apart from the obvious cases when $$L$$ is obtained from $$M$$ by a sequence of row interchanges, column interchanges, renaming of variables, and transposition? The answer was known to be no if $$n\leq 7$$; we show that it is yes for $$n=8$$. The Latin squares for which this situation occurs have interesting special characteristics.

##### MSC:
 05B15 Orthogonal arrays, Latin squares, Room squares
##### Keywords:
Latin square; determinant
GAP
Full Text:
##### References:
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