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In http://www.springerlink.com/content/y19u81675243r237/fulltext.pdf, 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} 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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    Good call, Qiaochu. Fixed.2011-02-01

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This question was answered at MathOverflow: https://mathoverflow.net/questions/54051/random-permutations-of-z-n