Zappa's extension of the Alon–Tarsi conjecture

Let a Latin square be normalized if its first row is the identity permutation and unipotent if all entries on its main diagonal are equal. Let $U_n^{\text{E}}$ and $U_n^{\text{O}}$ be the numbers of normalized unipotent even and odd Latin squares of order $n$, respectively, and define

$$AT(n):=U_n^{\text{E}}-U_n^{\text{O}}.$$

Zappa's extension of the Alon–Tarsi conjecture. For all $n$,

$$AT(n)\neq0.$$

This extends the Alon–Tarsi nonvanishing assertion to all orders by using normalized unipotent Latin squares; the source presents it as an extension proposed by Zappa, without resolving it in general.