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.

UR - http://www.scopus.com/inward/record.url?scp=0040523484&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0040523484&partnerID=8YFLogxK

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 -