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

翻译：我们证明，对于每一个偶数阶的简化奇数拉丁方，至少存在一个映射，使其像为同阶的简化偶数拉丁方。我们证明该映射是单射。因此，我们可以证明偶数阶偶数拉丁方的数量不小于同阶奇数拉丁方的数量。这为关于偶数拉丁方的Alon-Tarsi猜想给出了肯定答案。