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In, the author states the following without proof (equation 3.1):

Consider a random permutation $\pi$ of $\mathbb{Z}_n$. What is the probability that $\pi(i+1)-\pi(i) \pmod{n} <n/2$ for all $i$?

The claim is that this is $(2+o(1))^{-n}$, which makes sense and seems like it should be a standard argument. Does anyone have a formal proof?

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The maximum $\pi(i+1)- \pi(i)$ can be is $n-1$ in $\mathbb{Z}_n$. – PEV Jan 31 '11 at 23:09
I think you mean (2 + o(1))^{-n}? – Qiaochu Yuan Jan 31 '11 at 23:36
Good call, Qiaochu. Fixed. – Jeremy Hurwitz Feb 1 '11 at 6:21
up vote 2 down vote accepted

This question was answered at MathOverflow:

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