[R] Generating all possible partitions

[Gabor Grothendieck]

Yes, I just checked on Wikipedia and its as you say.

On 11/25/05, Ravi Varadhan <rvaradha at jhsph.edu> wrote:
> Isn't Bell number different from the number of partitions, P_n, of a number,
> n?
>
> Bell number, B_n, is the number of subsets into which a set with "n"
> elements can be divided.  So, B_3 = 5, and B_4 = 15, whereas P_3 = 3, and
> P_4 = 5.  Bell numbers grow much more rapidly than the number of partitions.
>
> Ravi.
>
> > -----Original Message-----
> > From: r-help-bounces at stat.math.ethz.ch [mailto:r-help-
> > bounces at stat.math.ethz.ch] On Behalf Of Gabor Grothendieck
> > Sent: Friday, November 25, 2005 1:10 PM
> > To: Ales Ziberna
> > Cc: R-help
> > Subject: Re: [R] Generating all possible partitions
> >
> > Probably not very fast but the number of partitions of a number,
> > also known as the Bell number, grows pretty dramatically so you
> > won't be able to use it for large numbers even with an efficient
> > implementation (though you could use it for larger numbers than
> > the solution here).  The main attribute of this approach is its
> > simplicity.   It generates the cartesian product
> > { 0, 1, 2, ..., n } ^ n and then picks off the elements that are
> > non-increasing and sum to n.
> >
> > n <- 3
> > g <- do.call("expand.grid", rep(list(0:n), n)) # cartesian product
> > f <- function(x) all(diff(x) <= 0) && sum(x) == length(x)
> > g[apply(g, 1, f), ]
> >
> >
> > On 11/25/05, Ales Ziberna <aleszib at gmail.com> wrote:
> > > I have posed this question earlier, however it has probably not been
> > clear
> > > enough.
> > >
> > >
> > >
> > > My problem is such. I would like to find all possible partitions of a
> > set of
> > > n objects into k groups. The ordering of the groups does not matter,
> > only
> > > which objects are together matters.
> > >
> > >
> > >
> > > For example, there are two possible partitions of 3 objects into 2
> > groups:
> > >
> > > 1 1 2
> > >
> > > 1 2 2
> > >
> > > By "the labels are not important" I meant that a partition 1 1 2 is
> > > identical to the partition 2 2 1.
> > >
> > >
> > > Best regards,
> > >
> > > Ales Ziberna
> > >
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> >
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