Two permutations $p$ and $q$ are equal if they are equal as functions, i.e., if $p(i) = q(i)$ for all $i$.
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We can also multiply (or compose) two permutations. We follow the convention of $(p*q)(i) = p(q(i))$.
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This also let's us compute powers of permutations.
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The source of this document is in Permutations/Documentation/packageDocs.m2:95:0.