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Topic: Conjecture about permutations
Replies: 4   Last Post: Jun 10, 2013 5:04 AM

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James Waldby

Posts: 348
Registered: 1/27/11
Re: Conjecture about permutations
Posted: Jun 8, 2013 12:38 PM
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On Sat, 08 Jun 2013 08:49:15 -0700, Vincent Granville wrote:

> An interesting conjecture about permutations is made in this article. Can you prove it? There's a reward for doing so.
>
> URL: http://www.analyticbridge.com/profiles/blogs/correlation-and-r-squared-for-big-data


Is the conjecture you refer to the one about whether q(n) = O(n)^{c+1},
stated in the paragraph that begins "I conjecture that..." ? Or is
it some other question?

On another topic: At the end of 2.2 you give an "Algorithm to generate
a random permutation (p(0), p(1), ... , p(n-1))" and ask, "what is the
computational complexity of this algorithm?". It is Theta(n log n),
as noted in <http://en.wikipedia.org/wiki/Coupon_collector%27s_problem>.

For a better random-permutation algorithm with Theta(n) performance,
use Fisher?Yates shuffle.
<http://en.wikipedia.org/wiki/Fisher%E2%80%93Yates_shuffle>

--
jiw



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