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Math Help - permutation questions

  1. #1
    Newbie
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    permutation questions

    Dear All.

    Can I ask something?

    There are two permutations

    x = (1 2 3 4 5 6 7 8)
    (3 5 2 1 4 6 8 7)

    y = (1 2 3 4 5 6 7 8)
    (6 1 5 7 3 2 8 4)

    Can I ask how I can express these as a product of transposition?
    I got a disjoint cycle for x (1 3 2 5 4) (7 8), then transposition is just (1 3) (3 2) (2 5) (5 4) (7 8)?
    And what is signature of both of them? I got odd for both of them.
    Is this correct?
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  2. #2
    MHF Contributor

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    Re: permutation questions

    Since (7 8) is already a transposition, we just need to focus on (1 3 2 5 4).

    I find that:

    (1 3)(3 2)(2 5)(5 4) = (1 3)(3 2)(2 5 4) = (1 3)(2 5 4 3) = (1 3 2 5 4), so you are correct. If you did y the same way congratulations!
    Thanks from boding
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