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Homework Help: Write as a Product of Transpositions

  1. Aug 14, 2011 #1
    1. The problem statement, all variables and given/known data
    Write the permutation
    P=
    12345678
    23156847
    
    in cycle notation, and then write it as a product of transpositions


    2. Relevant equations



    3. The attempt at a solution
    I got the cycle notation to be (123)(45687), but i am now not sure now to write it as a product of transpositions. My only really thought was just grouping the digits in twos but i don't think that is correct

    Thank you
     
  2. jcsd
  3. Aug 14, 2011 #2

    I like Serena

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    Homework Helper

    Welcome to PF, flufles! :smile:

    Each cycle can be written as a product of transpositions.
    The most common methods are:
    (1 2 3 4) = (1 4)(1 3)(1 2)
    and
    (1 2 3 4) = (1 2)(2 3)(3 4).
    See the pattern?
     
  4. Aug 14, 2011 #3
    thank you for the welcome,
    i think i do
    so (123) could be written as (12)(23) or (13)(12)
    and (45687) written as (45)(56)(68)(87) or (47)(48)(46)(45)
    and so would i just put these next to each other as (12)(23)(45)(56)(68)(87)

    Thank you
     
  5. Aug 14, 2011 #4

    I like Serena

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    Homework Helper

    Yep! That's it! :smile:

    And you're welcome.
     
  6. Aug 14, 2011 #5
    thank you very much =]
     
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