LOK asked in 科學及數學數學 · 1 decade ago

order of permutations

Dont know how to do the permutations

E.g (123)(12). If we do the permutation from the left first:

(123)(12)=(1)(23)=(23)

(1234)^2=(1234) (1234)=(13)(24)

What is the concept behind it???

2 Answers

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  • 1 decade ago
    Favorite Answer

    You can think them as the composition of two fn.(except the order of operation).

    (12): 1 -> 2, 2 -> 1

    (123): 1 -> 2, 2->3 , 3->1

    (123)(12): 1->2->1, 2->3, 3->1->2, so we obtain (1)(23) or (23)

    (1234)^2=(1234)(1234)

    1->2->3

    2->3->4

    3->4->1

    4->1->2

    so (1234)^2=(13)(24)

    2010-10-11 18:16:01 補充:

    1.

    Let f=(12), g=(123), then f。g=(123)(12).

    f。g: 1 -> f(2)=1

    f。g: 2 -> f(3)=3

    f。g: 3 -> f(1)=2

    so (123)(12)=f。g=(1)(23)=(23)

    2.

    f=(1234), (1234)^2=f。f

    f。f(1)=f(2)=3

    f。f(2)=f(3)=4

    f。f(3)=f(4)=1

    f。f(4)=f(1)=2

    so (1234)^2=f。f=(13)(24)

  • 1 decade ago

    Why we close the brakcet at 3?

    It is my thought: (1234)(1234)

    First bracket: 1->2, 2 in the first bracket ->3 in the second bracket. Why we closed bracket here? Why dont we keep on the rotation, like 3 in the second bracket -> 4 in the first bracket and 4 in the first bracket -> 1.

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