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Math Help - Random Permutation

  1. #1
    Senior Member Sampras's Avatar
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    Random Permutation

    Suppose  \pi is a random permutation of  \mathbb{Z}_n . How would you determine the probability that  \pi(i+1)-\pi(i) \pmod n < n/2 ? We know that  \pi(i+1)-\pi(i) is maximum at  n-1 in  \mathbb{Z}_n .
    Last edited by Sampras; January 31st 2011 at 04:11 PM.
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  2. #2
    Senior Member Sampras's Avatar
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    Perhaps we could use Inclusion-Exclusion? In other words, find the probability that  \pi(i+1)-\pi(i) > n/2 (i.e. the  i th and  i+1 -st places differ by more than  n/2 ?
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