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Math Help - permutation

  1. #1
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    permutation

    Can I ask one thing? I am really sorry.

    I have a = ( 1 2 3 4 5 6 7 ) and r = (1 2 3 4 5 6 7 )
    3 2 6 7 4 1 5 3 6 5 2 7 4 1

    if I want to get ar = should I start with r? so 1 -> 3 -> 6 ?

    or start with a?

    I thought I need to start with r, but some books says it starts with a

    But, those are different answers..

    Please help me out.
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  2. #2
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    Re: permutation

    Quote Originally Posted by yanirose View Post
    Can I ask one thing? I am really sorry.

    I have a = ( 1 2 3 4 5 6 7 ) and r = (1 2 3 4 5 6 7 )
    3 2 6 7 4 1 5 3 6 5 2 7 4 1

    if I want to get ar = should I start with r? so 1 -> 3 -> 6 ?

    or start with a?

    I thought I need to start with r, but some books says it starts with a

    But, those are different answers..

    Please help me out.
    ar(x) = a(r(x))

    so I think you should start with r as you've done i.e. 1 -> 3 -> 6, 2 -> 6 -> 1, etc.

    Product or Composite of Two Permutations
    Thanks from yanirose
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  3. #3
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    Re: permutation

    Hi, Thanks

    but the link you gave me says ar is a first and the r...?
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  4. #4
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    Re: permutation

    Quote Originally Posted by yanirose View Post
    Can I ask one thing? I am really sorry.

    I have a = ( 1 2 3 4 5 6 7 ) and r = (1 2 3 4 5 6 7 )
    3 2 6 7 4 1 5 3 6 5 2 7 4 1
    if I want to get ar = should I start with r? so 1 -> 3 -> 6 ?
    or start with a?
    I thought I need to start with r, but some books says it starts with a
    First of all make it readable.
    \alpha  = \left( {\begin{array}{*{20}{c}}1&2&3&4&5&6&7\\3&2&6&7&4&1  &5\end{array}} \right)\,\& \,\rho  = \left( {\begin{array}{*{20}{c}}1&2&3&4&5&6&7\\3&6&5&2&7&4  &1\end{array}} \right)

    There is no universal agreement of combining permutations. About one third of the sample textbooks that I reviewed say to use left/right order (that agrees with your textbook). All the rest say use function composition as in reply #2.

    If I were you however, I would follow the textbook, although I personally prefer the composition way.

    BTW: the authors who do the second way use the word composition, while the first way is often called product.
    Thanks from yanirose and romsek
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