all done

LouWatts — Fri, 16 Nov 2012 23:28:31 Z

never mind i've just done it... was a lot easier than I thought
its no where near polished but heres like the basic idea of it

MultiSetR:=[{2, 8}, {2, 4, 6, 7, 8}, {4, 6, 8}, {1, 4, 8}, {1, 4, 8, 9}];
for i from 1 to numelems(MultiSetR) do 
  for j from i+1 to numelems(MultiSetR) do 
    for k from j+1 to numelems(MultiSetR) do
       MultiSetR[i]:
       MultiSetR[j]:
       MultiSetR[k]:
       printf(" %a ,%a, %a \n", MultiSetR[i], MultiSetR[j], MultiSetR[k]):
    od:
  od:
od:

 {2, 8} ,{2, 4, 6, 7, 8}, {4, 6, 8} 
 {2, 8} ,{2, 4, 6, 7, 8}, {1, 4, 8} 
 {2, 8} ,{2, 4, 6, 7, 8}, {1, 4, 8, 9} 
 {2, 8} ,{4, 6, 8}, {1, 4, 8} 
 {2, 8} ,{4, 6, 8}, {1, 4, 8, 9} 
 {2, 8} ,{1, 4, 8}, {1, 4, 8, 9} 
 {2, 4, 6, 7, 8} ,{4, 6, 8}, {1, 4, 8} 
 {2, 4, 6, 7, 8} ,{4, 6, 8}, {1, 4, 8, 9} 
 {2, 4, 6, 7, 8} ,{1, 4, 8}, {1, 4, 8, 9} 
 {4, 6, 8} ,{1, 4, 8}, {1, 4, 8, 9}

combinat:-choose

Doug Meade — Mon, 19 Nov 2012 13:11:18 Z

The choose command in the combinat package will help you with this:

restart;
with(combinat):

S := [{2, 8}, {2, 4, 6, 7, 8}, {4, 6, 8}, {1, 4, 8}, {1, 4, 8, 9}];
 [{2, 8}, {2, 4, 6, 7, 8}, {4, 6, 8}, {1, 4, 8}, {1, 4, 8, 9}]

choose( S, 3 );
         [[{2, 8}, {1, 4, 8}, {4, 6, 8}], 

           [{2, 8}, {1, 4, 8}, {1, 4, 8, 9}], 

           [{2, 8}, {1, 4, 8}, {2, 4, 6, 7, 8}], 

           [{2, 8}, {4, 6, 8}, {1, 4, 8, 9}], 

           [{2, 8}, {4, 6, 8}, {2, 4, 6, 7, 8}], 

           [{2, 8}, {1, 4, 8, 9}, {2, 4, 6, 7, 8}], 

           [{1, 4, 8}, {4, 6, 8}, {1, 4, 8, 9}], 

           [{1, 4, 8}, {4, 6, 8}, {2, 4, 6, 7, 8}], 

           [{1, 4, 8}, {1, 4, 8, 9}, {2, 4, 6, 7, 8}], 

           [{4, 6, 8}, {1, 4, 8, 9}, {2, 4, 6, 7, 8}]]
nops( % );
                               10

choose( S );
[[], [{2, 8}], [{1, 4, 8}], [{4, 6, 8}], [{1, 4, 8, 9}], 

  [{2, 4, 6, 7, 8}], [{2, 8}, {1, 4, 8}], [{2, 8}, {4, 6, 8}], 

  [{2, 8}, {1, 4, 8, 9}], [{2, 8}, {2, 4, 6, 7, 8}], 

  [{1, 4, 8}, {4, 6, 8}], [{1, 4, 8}, {1, 4, 8, 9}], 

  [{1, 4, 8}, {2, 4, 6, 7, 8}], [{4, 6, 8}, {1, 4, 8, 9}], 

  [{4, 6, 8}, {2, 4, 6, 7, 8}], [{1, 4, 8, 9}, {2, 4, 6, 7, 8}], 

  [{2, 8}, {1, 4, 8}, {4, 6, 8}], 

  [{2, 8}, {1, 4, 8}, {1, 4, 8, 9}], 

  [{2, 8}, {1, 4, 8}, {2, 4, 6, 7, 8}], 

  [{2, 8}, {4, 6, 8}, {1, 4, 8, 9}], 

  [{2, 8}, {4, 6, 8}, {2, 4, 6, 7, 8}], 

  [{2, 8}, {1, 4, 8, 9}, {2, 4, 6, 7, 8}], 

  [{1, 4, 8}, {4, 6, 8}, {1, 4, 8, 9}], 

  [{1, 4, 8}, {4, 6, 8}, {2, 4, 6, 7, 8}], 

  [{1, 4, 8}, {1, 4, 8, 9}, {2, 4, 6, 7, 8}], 

  [{4, 6, 8}, {1, 4, 8, 9}, {2, 4, 6, 7, 8}], 

  [{2, 8}, {1, 4, 8}, {4, 6, 8}, {1, 4, 8, 9}], 

  [{2, 8}, {1, 4, 8}, {4, 6, 8}, {2, 4, 6, 7, 8}], 

  [{2, 8}, {1, 4, 8}, {1, 4, 8, 9}, {2, 4, 6, 7, 8}], 

  [{2, 8}, {4, 6, 8}, {1, 4, 8, 9}, {2, 4, 6, 7, 8}], 

  [{1, 4, 8}, {4, 6, 8}, {1, 4, 8, 9}, {2, 4, 6, 7, 8}], 

  [{2, 8}, {1, 4, 8}, {4, 6, 8}, {1, 4, 8, 9}, {2, 4, 6, 7, 8}]]
nops(%);
                               32

This finds the 10 three element subsets of this set of 5 sets. It also shows that there are a total of 32 different subsets with between 0 and 5 elements.

I hope this is still of some use to you.

Doug

---------------------------------------------------------------------
Douglas B. Meade  <><
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu
Phone:  (803) 777-6183         URL:    http://www.math.sc.edu

MaplePrimes - answers and comments on Question, How to get maple to output combinations (not the total)

all done

combinat:-choose