Determinants of latin squares of order 8

David Ford, Kenneth W. Johnson

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Abstract

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.

Original languageEnglish (US)
Pages (from-to)317-325
Number of pages9
JournalExperimental Mathematics
Volume5
Issue number4
DOIs
Publication statusPublished - Jan 1 1996

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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