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Difficult Question on Permutations

  1. Jan 31, 2009 #1
    If you have a permutation writtein disjoint cycle notation ( I attatched it )

    what's the minimum positive integer k such that t^k =Identity

    t is tau
     

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  3. Feb 1, 2009 #2

    CompuChip

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    Can you reason what will happen when [itex]\tau[/itex] is multiplied by itself? And if you calculate [itex]\tau^3[/itex]?
    What will happen in general when we keep multiplying tau by itself?
     
  4. Feb 1, 2009 #3
    Remember that disjoint cycles commute. Thus, if [itex]\tau = \tau_1 \tau_2 \dotsc \tau_m[/itex] is a product of disjoint cycles, then [itex]\tau^n = \tau_1^n \tau_2^n \dotsc \tau_m^n[/itex].
     
    Last edited: Feb 1, 2009
  5. Feb 1, 2009 #4

    CompuChip

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    Very well adrian, although I was sort of hoping PhysicsHelp12 would figure that out by himself.
     
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