LFD Book Forum Question 8: Growth function undetermined?

#1
04-28-2013, 10:13 PM
 binchen.bin@gmail.com Junior Member Join Date: Apr 2013 Posts: 7
Question 8: Growth function undetermined?

On question 8, the growth function m_H(N) seems to depend on the choice of q for any q<=N. Then m_H(N) is not determined by N solely? How to understand this situation?

Thanks.
#2
04-28-2013, 10:33 PM
 yaser Caltech Join Date: Aug 2009 Location: Pasadena, California, USA Posts: 1,477
Re: Question 8: Growth function undetermined?

Quote:
 Originally Posted by binchen.bin@gmail.com On question 8, the growth function m_H(N) seems to depend on the choice of q for any q<=N. Then m_H(N) is not determined by N solely? How to understand this situation? Thanks.
The value of does not change with . Fix a value for and try to derive a formula for the growth function given that . The formula will likely depend on the value that you fixed at, right? That dependency is what the problem is asking about.
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#3
07-08-2017, 03:01 PM
 Mike S Junior Member Join Date: Jul 2017 Posts: 1
Re: Question 8: Growth function undetermined?

I have formula of m(N) as:

$2^N - \sum_{k=0}^{N-1} 2^{N-1-k}\binom{k}{q}$

But not sure how to reduce to something tractable... Any suggestions please? Thanks.

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