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Math Help - Permutations

  1. #1
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    Permutations

    Consider the following permutation f in S6:

    f = 1 2 3 4 5 6
    .....6 1 3 5 4 2

    (The above is one set all in parentheses...)

    Calculate f^-1

    How do I do this?
    Last edited by jzellt; October 9th 2010 at 08:01 PM.
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  2. #2
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    Quote Originally Posted by jzellt View Post
    Consider the following permutation f in S6:

    f = 1 2 3 4 5 6
    .....6 1 3 5 4 2

    (The above is one set all in parentheses...)

    Calculate f^-1

    How do I do this?

    Read your permutation upside down...

    Thus, 1 |\rightarrow 2\,,\,2|\rightarrow  6 and etc.

    Tonio
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  3. #3
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    So, if I understand you correctly, this would be f^-1:

    f^-1 = 1 2 3 4 5 6
    ..........2 6 3 5 4 1

    Is this correct?
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  4. #4
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    Yes, that is fine. You could also write your group in the cycle notation as a product of disjoint cycles f=(1,6,2)(4,5). In this notation it's preferred not to write cycles that have only one entry. Any missing element is mapped to itself.

    f^{-1}=(1,6,2)^{-1}(4,5)^{-1}=(2,6,1)(5,4).

    which is the same as your answer in array notation.
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