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Math Help - permutations - help me understand please!

  1. #1
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    permutations - help me understand please!

    ok.. so I have two permutations:

    sigma 1:

    1->3, 2->2, 3->4, 4->1

    sigma 2:
    1->3, 2->4, 3->1, 4->2

    so sigma 1 = (1,3,4)
    sigma 2 = (1,3)(2,4)

    now find the compositions of sigma1sigma2
    and sigma2sigma1

    How do I do this?! I really dont understand which map you follow so to speak

    many thanks
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  2. #2
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    Quote Originally Posted by James0502 View Post
    ok.. so I have two permutations:

    sigma 1:

    1->3, 2->2, 3->4, 4->1

    sigma 2:
    1->3, 2->4, 3->1, 4->2

    so sigma 1 = (1,3,4)
    sigma 2 = (1,3)(2,4)

    now find the compositions of sigma1sigma2
    and sigma2sigma1

    How do I do this?! I really dont understand which map you follow so to speak

    many thanks
    \sigma_1 \sigma_2=(1,3,4)(1,3)(2,4)

    Now lets simplify this by computing the permutation.

    so lets immagine sending 1 in on the right ...
    1 goes through (2,4) unchanaged.
    1 goes into (1,3) and comes out 3
    3 goes into (1,3,4) and comes out 4

    so 1 goes to 4 (1,4

    Now lets send 4 in

    4 goes into (2,4) and comes out 2
    2 goes into (1,3) and is unchanged.
    2 goes into (1,3,4) and is unchanges

    so 4 goes to 2 (1,4,2

    Now lets send 2 in

    2 goes into (2,4) and comes out 4
    4 goes into (1,3) and is unchanged
    4 goes into (1,3,4) and comes out 1

    so 2 goes to 1 (1,4,2)

    Now the only number we didn't check in are chain is 3.

    if you check it 3 goes to 3.

    so we end up with

    \sigma_1 \sigma_2=(1,3,4)(1,3)(2,4)=(1,4,2)
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  3. #3
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    Quote Originally Posted by TheEmptySet View Post
    \sigma_1 \sigma_2=(1,3,4)(1,3)(2,4)
    While I agree that this is the mathematical correct to consider compositions of the permutation mappings, unfortunately there textbooks/authors that do not use this convention, they use left-to-right composition. So please check the definition of the textbook used.
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