## Experimental Mathematics

### Determinants of Latin squares of order {$8$}

#### Abstract

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.

#### Article information

Source
Experiment. Math., Volume 5, Issue 4 (1996), 317-325.

Dates
First available in Project Euclid: 13 March 2003

Ford, David; Johnson, Kenneth W. Determinants of Latin squares of order {$8$}. Experiment. Math. 5 (1996), no. 4, 317--325. https://projecteuclid.org/euclid.em/1047565449