1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    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

    User Avatar
    Homework Helper

    Yep! That's it! :smile:

    And you're welcome.
     
  6. Aug 14, 2011 #5
    thank you very much =]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Write as a Product of Transpositions
Loading...