Re: minimum of a function into two variables

Robert Israel <israel@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx> wrote:
David W. Cantrell <DWCantrell@xxxxxxxxxxx> writes:

Andrea <acirulli@xxxxxxxxx> wrote:
Hi,
I need some suggestion,
Let P_s=p!/{n choose p}

I assume that your n and p are positive integers; let us know if that
is not the case.

I need to calculate fixing P_s (for example P_s=2^-12) the minimum of
this function:
f(x)=p+ p \times \log{n}

I don't suppose you meant f(x), since x hasn't been mentioned
elsewhere; rather, you wish to minimize p(1 + log(n)). Is that correct?

You say that P_s is fixed and give P_s = 2^-12 as an example. But,
assuming that n and p are positive integers, I suspect it not possible
to have P_s = 2^-12 exactly.

You could take n = 2^12 and p = 1.

Oops! Of course. I should have realized that. It's the trivial case:
If P_s = 1/m for positive integer m, then we can always take n = m and
p = 1.

Now I wonder if there are any nontrivial solutions when P_s = 2^-12.

David
.

Relevant Pages

  • Re: minimum of a function into two variables
    ... David W. Cantrell writes: ... I need some suggestion, ... assuming that n and p are positive integers, ...
    (sci.math)
  • Re: minimum of a function into two variables
    ... Andrea wrote: ... I need some suggestion, ... assuming that n and p are positive integers, ... I suspect that there are no more possible pairs. ...
    (sci.math)
  • Re: minimum of a function into two variables
    ... I need some suggestion, ... I assume that your n and p are positive integers; let us know if that is ... David W. Cantrell ... Oh yeah this is a wrong example, I want to say that i want to choose ...
    (sci.math)
  • Re: minimum of a function into two variables
    ... Andrea wrote: ... I need some suggestion, ... I assume that your n and p are positive integers; let us know if that is ... David W. Cantrell ...
    (sci.math)
  • Re: elementary number theory result
    ... Robert Israel wrote: ... > James Pirk wrote: ... >> I am reading a paper which states a number theory result to show ... >> Let P be a subset of positive integers closed under addition. ...
    (sci.math)
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