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Math Help - Probabilistic Group Theory

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    Probabilistic Group Theory

    Prove that the probability that two elements of the symmetric group S_n, chosen randomly with replacement, commute is \frac{P(n)}{n!}, where P(n) is the partition function.
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    Senior Member Sampras's Avatar
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    Quote Originally Posted by NonCommAlg View Post
    Prove that the probability that two elements of the symmetric group S_n, chosen randomly with replacement, commute is \frac{P(n)}{n!}, where P(n) is the partition function.
     P(n) is the number of cycle types of  S_n . And the number of cycle types is the number of ways of choosing two elements of  S_n that commute.
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