What is the average length of the longest increasing subsequence of a random permutation of the first n natural numbers?

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    $\begingroup$ IIRC, this is asymptotic as $2\sqrt{n}$. Don't think there is a known closed form. $\endgroup$ – Macavity Mar 31 '13 at 6:45
  • $\begingroup$ @Macavity do you know a reference for this fact ? $\endgroup$ – Ewan Delanoy Mar 31 '13 at 6:59
  • $\begingroup$ @ewanDelanoy search for aldous & diaconis, 1995 Don't have the exact reference handy. $\endgroup$ – Macavity Mar 31 '13 at 7:21
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    $\begingroup$ Ok - here it is. $\endgroup$ – Macavity Mar 31 '13 at 7:43

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