Well here is one way (but this finds too many, then reduces, so if the final result is near the memory limit, this would go over first):
unique(t(combn( rep(LETTERS[1:5], each=2), 3))) -- Gregory (Greg) L. Snow Ph.D. Statistical Data Center Intermountain Healthcare greg.s...@imail.org 801.408.8111 > -----Original Message----- > From: r-help-boun...@r-project.org [mailto:r-help-boun...@r- > project.org] On Behalf Of Ted Harding > Sent: Thursday, June 24, 2010 2:53 PM > To: Doran, Harold > Cc: r-help@r-project.org > Subject: Re: [R] [OT] Combinatorials wtih constraints > > On 24-Jun-10 19:47:38, Doran, Harold wrote: > > This is not an R question, but a question on some combinatorial > > mathematics. Apologies for the OT if it is wildy inappropriate. > > The traditional C(n.k) method tells me how many combinations k > > I can make with n objects. However, suppose I want the number of > > combinations where an object cannot be used more than Q times > > where Q is a parameter that changes? > > > > For instance: > > > > combn(LETTERS[1:5], 3) > > > > shows the number of triplets I can make with the 5 letters. > > But, suppose I want the constraint that no letter can be used > > more than twice (Q). > > > > Are there well-known methods for identifying the number of possible > > combinations with this kind of constraint? > > > > Thanks, > > Harold > > I think there is some confusion in the statement of the problem. > "C(n,k)" gives the number of ways of choosing k distinct objects > out of n distinct objects, so there is no repetition of an object > in any of the selections of k objects. This can be observed in the > result of your "combn(LETTERS[1:5], 3)" command: > > combn(LETTERS[1:5], 3) > # [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] > # [1,] "A" "A" "A" "A" "A" "A" "B" "B" "B" "C" > # [2,] "B" "B" "B" "C" "C" "D" "C" "C" "D" "D" > # [3,] "C" "D" "E" "D" "E" "E" "D" "E" "E" "E" > > So no letter is used more than once, let alone more than twice, > so it is maximally constrained! > > Is it the case that your question is > > In how many ways can we choose k objects out of n distinct > objects, with repetition allowed, but with no more than Q > replicates of any object in the selection? > > If so, I'm not sure whether there is an R function which will > handle it directly, and as a combinatorial problem it is one > where you can quite easily drop stitches; so if there isn't > one I'll wait for confirmation before thinking about how to > implement it in R! > > There may be some mileage in the 'partitions' package, see e.g. > > http://finzi.psych.upenn.edu/R/library/partitions/html/ > partitions.package.html > > but I think one would need to experiment with it a bit in order > to be sure what the functions do. > > Ted. > > -------------------------------------------------------------------- > E-Mail: (Ted Harding) <ted.hard...@manchester.ac.uk> > Fax-to-email: +44 (0)870 094 0861 > Date: 24-Jun-10 Time: 21:51:49 > ------------------------------ XFMail ------------------------------ > > ______________________________________________ > R-help@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting- > guide.html > and provide commented, minimal, self-contained, reproducible code. ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
