Why does Sattolo's algorithm produce a permutation with exactly one cycle?
On creating a single-cycle permutation from a shuffle:<p>Take 0, 1, 2, 3, 4, 5 and shuffle it.
4, 3, 0, 5, 1, 2<p>Now you can read out a permutation:<p>4 → 3<p>3 → 0<p>0 → 5<p>5 → 1<p>1 → 2<p>2 → 4<p>It will only have one cycle.