So I was reading up about the derangement recurrence relation proven in a combinatorical way. The proof I was looking at is at this webpage. The combinatorical proof is at the bottom of the page below the algebraic proofs.(adsbygoogle = window.adsbygoogle || []).push({});

"ttp://planetmath.org/?op=getobj&from=objects&id=11991"[/URL]

So in this proof the part I'm not understanding is:[QUOTE]Adding n before any of the n−1 elements of produces a derangement of [n] .[/QUOTE]

It seems to me this doesn't always lead to a derangement of [n]. Such in the case of (2, 1, 5, 4, 3). If you add 6 before 2 then you get (6, 2, 1, 5, 4, 3), which is no longer a derangement. What am I missing that I'm not understanding this?

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# Derangement Recurrence Relation Proof Doesn't Seem To Make Sense

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