TY - JOUR

T1 - Determinants of latin squares of order 8

AU - Ford, David

AU - Johnson, Kenneth W.

N1 - Funding Information:
This research was supported by the Natural Sciences and Engineering Research Council (Canada) and Fonds pour la Formation de Chercheurs et l'Aide a la Recherche (Quebec). The work was carried out while the second author was visiting the Computer Science Department of Concordia University and thanks are due for the hospitality extended. The authors wish to acknowledge the initial suggestion of John McKay that the calculation was feasible, and also to thank Clement Lam and Alexander Hulpke for their generous assistance in preparing the table of mapping and automorphism groups.

PY - 1996

Y1 - 1996

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

SN - 1058-6458

VL - 5

SP - 317

EP - 325

JO - Experimental Mathematics

JF - Experimental Mathematics

IS - 4

ER -