Re: A combinatorial question

On 10/2/07, Alasdair McAndrew wrote:
> To experiment with a little algorithm, I need to generate all subsets of a
> set S which have fixed cardinality; for example to generate all three
> element subsets of {1,2,3,4,5,6,7}.  Is there an inbuilt command to do this
> in Axiom?  Or has somebody written a package to do such a thing?
>

Here is one possible solution using the subSet operation:

(1) -> subsets(s,n) == set [set map(i+->parts(s).(i+1),j) for j in [subSet(#s,n,
k) for k in 0..binomial(#s,n)-1]]
                                         Type: Void

(2) -> subsets(expand(1..7),3)
   Compiling function subsets with type (List Integer,PositiveInteger)
       -> Set Set Integer

   (2)
   {{1,2,3}, {1,2,4}, {1,3,4}, {2,3,4}, {1,2,5}, {1,3,5}, {2,3,5}, {1,4,5},
    {2,4,5}, {3,4,5}, {1,2,6}, {1,3,6}, {2,3,6}, {1,4,6}, {2,4,6}, {3,4,6},
    {1,5,6}, {2,5,6}, {3,5,6}, {4,5,6}, {1,2,7}, {1,3,7}, {2,3,7}, {1,4,7},
    {2,4,7}, {3,4,7}, {1,5,7}, {2,5,7}, {3,5,7}, {4,5,7}, {1,6,7}, {2,6,7},
    {3,6,7}, {4,6,7}, {5,6,7}}
                                      Type: Set Set Integer

Regards,
Bill Page.