TY - JOUR
T1 - Determinants of latin squares of order 8
AU - Ford, David
AU - Johnson, Kenneth W.
PY - 1996/1/1
Y1 - 1996/1/1
N2 - A latin square is an n × 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 ≤ 7; we show that it is yes for n = 8. The Latin squares for which this situation occurs have interesting special characteristics.
AB - A latin square is an n × 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 ≤ 7; 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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U2 - 10.1080/10586458.1996.10504596
DO - 10.1080/10586458.1996.10504596
M3 - Article
AN - SCOPUS:0040523484
VL - 5
SP - 317
EP - 325
JO - Experimental Mathematics
JF - Experimental Mathematics
SN - 1058-6458
IS - 4
ER -