## Experimental Mathematics

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

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

David Ford and Kenneth W. Johnson

#### 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

**Permanent link to this document**

https://projecteuclid.org/euclid.em/1047565449

**Mathematical Reviews number (MathSciNet)**

MR1437221

**Zentralblatt MATH identifier**

0876.05017

**Subjects**

Primary: 05B15: Orthogonal arrays, Latin squares, Room squares

Secondary: 15A15: Determinants, permanents, other special matrix functions [See also 19B10, 19B14]

#### Citation

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