give all combinations

Yuan Jian, sending 9 emails within the span of few seconds all with 
similar text is very confusing to say the least!

Carl, look up combinations() and permutations() in the gtools package.


For two case scenario, you can use combinations()

    v <- c("a","b","c")

    library(gtools)
    tmp <- combinations(3, 2, v,repeats=TRUE)
    apply( tmp, 1, paste, collapse="" )
    [1] "aa" "ab" "ac" "bb" "bc" "cc"


For more than two cases, I don't know of an elegant way except to 
generate all possible permutations and then eliminate those with the 
same ingredients. This function will be slow for large numbers!


    multiple.combinations <- function( vec, times ){

       input <- vector( mode="list", times )
       for(i in 1:times) input[[i]] <- vec

       out <- expand.grid( input )
       out <- apply( out, 1, function(x) paste( sort(x), collapse="" ) )
       unique.out <- unique(out)
       return(unique.out)
    }

   multiple.combinations( v, 3 )
   [1] "aaa" "aab" "aac" "abb" "abc" "acc" "bbb" "bbc" "bcc" "ccc"

   multiple.combinations( v, 6 )
   "aaaaaa" "aaaaab" "aaaaac" "aaaabb" "aaaabc" "aaaacc" "aaabbb"
   "aaabbc" "aaabcc" "aaaccc" "aabbbb" "aabbbc" "aabbcc" "aabccc"
   "aacccc" "abbbbb" "abbbbc" "abbbcc" "abbccc" "abcccc" "accccc"
   "bbbbbb" "bbbbbc" "bbbbcc" "bbbccc" "bbcccc" "bccccc" "cccccc"

Regards, Adai

I seem to be missing something here:

given a set X:{a,b,c,whatever...}
the mathematical definition of 'permutation' is the set of all possible 
sequences of the elements of X.
The definition of 'combination' is all elements of 'permutation' which 
cannot be re-ordered to become a different element.

example:  X:{a,b,c}

perm(X) = ab, ab, bc, ba, ca, cb
comb(X) = ab, ac, bc


So maybe a better question for this mailing list is:  Are there 
functions available in any R package which produce perm() and comb() 
(perhaps as well as other standard combinatoric functions) ?

Carl

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"CW" == Carl Witthoft <carl at witthoft.com>
    on Mon, 01 Sep 2008 12:19:07 -0400 writes:

CW> I seem to be missing something here:
    CW> given a set X:{a,b,c,whatever...}
    CW> the mathematical definition of 'permutation' is the set of all possible 
    CW> sequences of the elements of X.
    CW> The definition of 'combination' is all elements of 'permutation' which 
    CW> cannot be re-ordered to become a different element.

    CW> example:  X:{a,b,c}

    CW> perm(X) = ab, ab, bc, ba, ca, cb
    CW> comb(X) = ab, ac, bc


    CW> So maybe a better question for this mailing list is:  Are there 
    CW> functions available in any R package which produce perm() and comb() 
    CW> (perhaps as well as other standard combinatoric functions) ?

combn()  has been "standard R"  for quite a while now.

As others have mentioned in this thread (different branch of
same thread-tree), for permutations, one can typically easily
get what one wants  via  expand.grid() or  outer()  [or
mapply() .. ].
For that reason, those knowing R well haven't seen a big need
for a permutation() function.

Martin Maechler, ETH Zurich and R Core Team