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: [EMAIL PROTECTED] [mailto:r-help- > [EMAIL PROTECTED] 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 <[EMAIL PROTECTED]> 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 > > > > ______________________________________________ > > [email protected] mailing list > > https://stat.ethz.ch/mailman/listinfo/r-help > > PLEASE do read the posting guide! http://www.R-project.org/posting- > guide.html > > > > ______________________________________________ > [email protected] mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide! http://www.R-project.org/posting- > guide.html ______________________________________________ [email protected] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
