# The many formulae that count Latin squares

#### by Douglas S Stones

Institution: Monash University
Date: Tue 11th May 2010
Time: 2:15 PM
Location: Room 215, Richard Berry Building, The University of Melbourne

Abstract: A Latin square is an $n \times n$ matrix containing
$n$ distinct symbols such that each row and each column
contains each symbol exactly once. Latin squares are widely
used for designing experiments and in error-correcting codes.
However, merely counting Latin squares poses a significant
problem and many prior attempts have subsequently been
proved faulty. Despite some claims to the contrary, there are
many formulae for the number of Latin squares. In this talk,
we will give a survey of these formulae and their history which
stretches all the way back to MacMahon in 1898!