[R] generating unordered combinations

[William Dunlap]

There is a 1-1 correspondance between your n-sets
consisting of m possible element types (0 through m-1
in your example) and the number of n-subsets of a (n+m-1)-set.
E.g., your example had m=3 and n=3 and subtracting
1:3 from each column of combn(3+3-1,3) gives your result:

>  t(combn(3+3-1, 3)-(1:3))
      [,1] [,2] [,3]
 [1,]    0    0    0
 [2,]    0    0    1
 [3,]    0    0    2
 [4,]    0    1    1
 [5,]    0    1    2
 [6,]    0    2    2
 [7,]    1    1    1
 [8,]    1    1    2
 [9,]    1    2    2
[10,]    2    2    2

Bill Dunlap
TIBCO Software Inc - Spotfire Division
wdunlap tibco.com  

> -----Original Message-----
> From: r-help-bounces at r-project.org 
> [mailto:r-help-bounces at r-project.org] On Behalf Of Dan Halligan
> Sent: Thursday, September 17, 2009 1:31 PM
> To: r-help at r-project.org
> Subject: [R] generating unordered combinations
> 
> Hi,
> 
> I am trying to generate all unordered combinations of a set of
> numbers / characters, and I can only find a (very) clumsy way of doing
> this using expand.grid.  For example, all unordered combinations of
> the numbers 0, 1, 2 are:
> 0, 0, 0
> 0, 0, 1
> 0, 0, 2
> 0, 1, 1
> 0, 1, 2
> 0, 2, 2
> 1, 1, 1
> 1, 1, 2
> 1, 2, 2
> 2, 2, 2
> 
> (I have not included, for example, 1, 0, 0, since it is equivalent to
> 0, 0, 1).
> 
> I have found a way to generate this data.frame using expand.grid as
> follows:
> 
> g <- expand.grid(c(0,1,2), c(0,1,2), c(0,1,2))
> for(i in 1:nrow(g)) {
> 	g[i,] <- sort(as.character(g[i,]))
> }
> o <- order(g$Var1, g$Var2, g$Var3)
> unique(g[o,]).
> 
> This is obviously quite clumsy and hard to generalise to a greater
> number of characters, so I'm keen to find any other solutions.  Can
> anyone suggest a better (more general, quicker) method?
> 
> Cheers
> 
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