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Help with permutation cycles

  1. Jan 23, 2005 #1


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    can anyone explain me the technique to decompose a random n-cycle into a bucnh of 2 cycles. Thanks in advance.
  2. jcsd
  3. Jan 23, 2005 #2
    Look at: (ab)(ac). Approaching this from the left, we have (1) a goes to b. (2) b goes to a in cycle one, and then a goes to c in cycle two. (3) As for c it is sent into a, cycle two.

    Thus (abc)=(ab)(ac). And so forth, (abcd) = (ab)(ac)(ad), etc.
    Last edited: Jan 23, 2005
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