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Math Help - Permutation confusion

  1. #1
    Senior Member slevvio's Avatar
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    Permutation confusion

    any enlightenment about this would be great I dont know whether the permutation moves A to where B is in the first picture or if we apply the function to A it becomes C.


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  2. #2
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    Quote Originally Posted by slevvio View Post
    any enlightenment about this would be great I dont know whether the permutation moves A to where B is in the first picture or if we apply the function to A it becomes C.



    Is the one from the left: why do you think it could be the right one, anyway??

    Tonio
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  3. #3
    Senior Member slevvio's Avatar
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    because A goes to where B is in the original triangle, B goes to where C is and C goes to where A is

    also this is meant to be an example of one of the rotations in the dihedral group for an equilateral triangle
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    Quote Originally Posted by slevvio View Post
    because A goes to where B is in the original triangle, B goes to where C is and C goes to where A is

    Oops! Now that you say that I see both possibilities can happen. I guess it all depends on definitions: are we to understand that the vertices are moved (together with their tag = letter) or else the vertices are kept fixed and we move only the letters??
    In the first case the right option is correct, since vertex A is moved to position prviously occupied by vertex B, but in the second case the left one is the correct one.

    Tonio
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  5. #5
    Senior Member slevvio's Avatar
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    hehe thanks also those two are inverses of each other which is interesting hehe. I will find out what convention gets used at this university but thanks for the help
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  6. #6
    Super Member Matt Westwood's Avatar
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    It's not something to get hung up on - the group S_3 = D_3 or whatever it gets called is generally used only for training purposes, as are the diagrams that illustrate the permutations. So whichever convention is being used, you'll be off them quicker than training wheels on your first pushbike.
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