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Longest increasing subsequence

  1. Nov 23, 2012 #1

    "Let [itex]x_1, ..., x_n[/itex] be i.i.d random variables uniformly on [0,1]. Let [itex]X[/itex] be the length of the longest increasing subsequence of [itex]x_1, ..., x_n[/itex]. Show that [itex]E[X] \ge (1-o(1))(1-e^{-1}) \sqrt{n}[/itex]."

    Hi forum!

    Using the Erdos' lemma I can only deduce that [itex]E[X] \ge \frac{1}{2} \sqrt{n}[/itex], which is a weaker bound unfortunately.

    I would appreciate any further ideas!

    Thanks for your help,
  2. jcsd
  3. Nov 23, 2012 #2

    Stephen Tashi

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    Science Advisor

    What does the notation "[itex] o(1) [/itex]" mean in this context?
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