Latin square enumeration
= Latin square enumeration
{title2=$n^{n^2}\quad\text{or}\quad(n!)^n$}
Enumerating every <Latin square> of a specified order, without identifying row, column or symbol <permutations> as the same output. Arbitrary square generation visits $n^{n^2}$ candidates. Restricting every row to a <permutation> reduces this to $(n!)^n$ candidates. Both counts follow by independent choices for positions or rows; neither count is the number of valid <Latin squares>.