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Longest increasing subsequence 
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#1
Nov2312, 09:12 AM

P: 1

Problem:
"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 (1o(1))(1e^{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, Michael 


#2
Nov2312, 07:25 PM

Sci Advisor
P: 3,252

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



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