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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.

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  • $\begingroup$ I'd call it a set of pairwise non-intersecting permutations. I'd even perhaps call it a non-intersecting family. Not a big fan of "totally non-intersecting." $\endgroup$
    – Pat Devlin
    Dec 17, 2016 at 7:48

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These are mutual derangements. Equivalently, the rows of a latin rectangle. Probably other names have appeared.

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