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Thread: Composite permutation multiplication

  1. #1
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    Composite permutation multiplication

    In the following composite permutation multiplication I got the value 1 repeatedly. Is it true? If false, plz explain me....

    ....| 2 1 4 6 | | 6 5 1 9 | | 2 1 3 4 | | 6 9 |
    g=| 1 4 6 2 | | 5 1 9 6 | | 1 3 9 6 | | 9 6 | means g=( 2 1 4 6 ) ( 6 5 1 9 ) ( 2 1 3 4 ) ( 6 9 )

    ...| 2 6 5 1 7 | | 6 1 2 5 4 3 | |2 4 6 7 |
    f=| 6 5 1 7 2 | | 1 2 5 4 3 6 | |4 6 7 2 | means f= ( 2 6 5 1 7 ) ( 6 1 2 5 4 3 ) (2 4 6 7 )


    g o f= | 1 2 3 4 5 .......|
    .........| 2 6 4 1 1 .......|

    Plz reply me as soon as possible

    Thanks,
    Sophia
    Last edited by ranyeng; Apr 6th 2010 at 01:03 PM.
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  2. #2
    MHF Contributor
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    Permutations are bijections, in particular, injections. So two different numbers cannot be mapped to 1.
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