On Jan 24, 2008 3:32 PM, Brian Granger <[EMAIL PROTECTED]> wrote:
>
> > > Question: where would we begin looking to see if this algorithm is
> > > known already?
> >
> >
> > Let a(m,n) be the number of multiplicative partitions of integers into m
> > parts.
> >
> > For m fixed, compute a(m,n) for n = 3,4,5... and search for this sequence
> > in Sloane's encyclopedia.
> >
> > And, let b(n) = sum([a(m,n) for m = [1..n]]); also search for this
> > sequence. Often, even relatively recent research is known to Sloane's
> > tables.
>
> Isn't this (the question of how many such partitions exist) really a
> separate question from how you actually calculate exactly what those
> partitions are? In our case, knowing how many exist is not enough, we
> actually need all of them. Am I missing something?
>
I think Tom just meant the above as a hint to answer the question
"where would we begin looking to see if this algorithm is known already?"
Sloane's tables of integer sequences:
http://www.research.att.com/~njas/sequences/
contain a _lot_ of references to the literature and research.
So Tom took the problem you've solved, extracted an
integer sequence out of it, and is suggesting that if you search
for research on that sequence, who knows, maybe you'll
find that somebody computed those numbers by actually
enumerating all partitions, or at least somebody doing research
on those numbers also did research on ways to enumerate
all partitions.
William
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