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fixed typo
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Igor Rivin
Igor Rivin
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That the probability is at least $O(1/n^2$$O(1/n^2)$ is immediate, since the probability that both permutations are $n$-cycles is $1/n^2.$ For the upper bound, there is a convergence speed estimate by Zacharovas, see in particular theorems 3 and 4, which should give you what you want.

That the probability is at least $O(1/n^2$ is immediate, since the probability that both permutations are $n$-cycles is $1/n^2.$ For the upper bound, there is a convergence speed estimate by Zacharovas, see in particular theorems 3 and 4, which should give you what you want.

That the probability is at least $O(1/n^2)$ is immediate, since the probability that both permutations are $n$-cycles is $1/n^2.$ For the upper bound, there is a convergence speed estimate by Zacharovas, see in particular theorems 3 and 4, which should give you what you want.

Source Link
Igor Rivin
Igor Rivin
  • 96.4k
  • 11
  • 153
  • 366

That the probability is at least $O(1/n^2$ is immediate, since the probability that both permutations are $n$-cycles is $1/n^2.$ For the upper bound, there is a convergence speed estimate by Zacharovas, see in particular theorems 3 and 4, which should give you what you want.