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1996 Determinants of Latin squares of order {$8$}
David Ford, Kenneth W. Johnson
Experiment. Math. 5(4): 317-325 (1996).


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 $n\le7$; we show that it is yes for $n=8$. The latin squares for which this situation occurs have interesting special characteristics.


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David Ford. Kenneth W. Johnson. "Determinants of Latin squares of order {$8$}." Experiment. Math. 5 (4) 317 - 325, 1996.


Published: 1996
First available in Project Euclid: 13 March 2003

zbMATH: 0876.05017
MathSciNet: MR1437221

Primary: 05B15
Secondary: 15A15

Rights: Copyright © 1996 A K Peters, Ltd.


Vol.5 • No. 4 • 1996
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