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-   -   Does dichotomy require growth function=2 for N=1? (http://book.caltech.edu/bookforum/showthread.php?t=929)

Thomaseid 07-30-2012 11:02 PM

Does dichotomy require growth function=2 for N=1?
 
According to the definition of dichotomy, is it that at least for one point, there should be two ways to label this only point (+1 or -1), thus growth function=2 is required for N=1? Is this statement correct?

I am thinking that for iii) and iv) in Q5, these two growth function=1 for N=1, which excludes them from the space of growth functions (in addition to the polynomial or 2^N criteria). Please advice whether it is the right alternative way for solving Q5.

Thanks.

yaser 07-31-2012 12:13 AM

Re: Does dichotomy require growth function=2 for N=1?
 
Quote:

Originally Posted by Thomaseid (Post 3748)
According to the definition of dichotomy, is it that at least for one point, there should be two ways to label this only point (+1 or -1), thus growth function=2 is required for N=1? Is this statement correct?

A dichotomy is a single pattern of \pm 1's on the N points. It does not say anything about other patterns that may be valid on these points, so there is no implication on the value of the growth function.

Thomaseid 07-31-2012 08:40 AM

Re: Does dichotomy require growth function=2 for N=1?
 
Thank you. Got it.


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