I'm learning permutations and came upon this question which made me freeze. So to say it in my own words, it asks that how many permutations in $S_n$ do not have a cycle of length one in their disjoint cycle notation. My guess at it would be just one but I don't know how to show it.

  • $\begingroup$ Have you tried writing down all the permutations of $S_3$ as products of disjoint cycles? $\endgroup$ – Paul Gustafson Apr 10 '13 at 14:18
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    $\begingroup$ Tough problem, if you are meeting it fresh. Look at the wikipedia article on Derangements. $\endgroup$ – André Nicolas Apr 10 '13 at 14:22
  • $\begingroup$ @AndréNicolas I looked at Derangments but it confused me further. I can see the connection to a certain limit but Im not able to solve for this problem. $\endgroup$ – user65422 Apr 14 '13 at 23:48
  • $\begingroup$ @user66345 Like this? $(a,b,c)=(a,c),(a,b)$ $\endgroup$ – user65422 Apr 15 '13 at 1:18

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