  We show that for each reduced odd latin square of even order there exists at
least one map such that its image is a reduced even latin square of the same
order. We prove that this map is injective. As a consequence, we can show that
the number of even latin squares of even order is bounded from below by the
number of odd latin squares of the same order. This gives a positive answer to
the Alon-Tarsi conjecture on even latin squares
