Determinants of Latin squares of order {$8$}
Ford, David ; Johnson, Kenneth W.
Experiment. Math., Tome 5 (1996) no. 4, p. 317-325 / Harvested from Project Euclid
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.
Publié le : 1996-05-14
Classification:  05B15,  15A15
@article{1047565449,
     author = {Ford, David and Johnson, Kenneth W.},
     title = {Determinants of Latin squares of order {$8$}},
     journal = {Experiment. Math.},
     volume = {5},
     number = {4},
     year = {1996},
     pages = { 317-325},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1047565449}
}
Ford, David; Johnson, Kenneth W. Determinants of Latin squares of order {$8$}. Experiment. Math., Tome 5 (1996) no. 4, pp.  317-325. http://gdmltest.u-ga.fr/item/1047565449/