The term "intersecting permutations" is used for a family of permutations $A \subset S\_n$ such that for all $\pi,\sigma \in A$, $\pi(i)=\sigma(i)$ for some $i \in [n]$. 


Is there a term for a family of permutations with the "opposite" property, that is for all $\pi,\sigma \in A$, $\pi(i)\neq \sigma(i)$ for all $i \in [n]$? These families are obviously non-intersecting, but clearly not every non-intersecting family has this property.



Common name for totally non-intersecting permutations
These are mutual derangements. Equivalently, the rows of a latin rectangle. Probably other names have appeared.


