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Cycle permutation

  1. Sep 21, 2011 #1
    I feel like I'm doing this correctly but my professor gave us an answer that is different from what I'm getting.

    Composition of (12345)(12345)

    Reading right to left I get (13524) but the answer he gives is (135)(24)

    The odd thing is I'm getting the rest of these correct so I dont feel like I'm doing it wrong.
     
  2. jcsd
  3. Sep 21, 2011 #2

    lanedance

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    Homework Helper

    actually scratch that, made an error will get back to you
     
  4. Sep 21, 2011 #3

    lanedance

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    so just to be clear on notation, as it can get tricky I read p=(123) as acting as follows
    p(1)=2
    p(2)=3
    p(3)=1

    so applying this to the 3 case gives
    (123) 123
    =231

    and note
    (123)=(231)=(312)

    so applying this in your case
    (12345) 12345
    =23451
    (12345) 23451
    34512

    so we have
    12345
    34512

    which gives (13524), same as you

    not applying (135)(24) gives
    (135) 12345
    =32541
    (24) 32541
    34521
    which is not the same

    sorry for the alignment, can't get it to work
     
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