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Help on Partitions, Again!!!

• To: mathgroup at smc.vnet.net
• Subject: [mg24636] Help on Partitions, Again!!!
• From: Jose Prado de Melo <jpmelo at iconet.com.br>
• Date: Fri, 28 Jul 2000 17:24:28 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

Hello, MathGroup
First of all, thanks for your attention.
To be more specific:
It's not too dificult to calculate the solution of the problem:
How many ways, can the set {A,B,C,D,E,F} be separeted into two parts
with three elements in each?
 Answer:   x = 6!/(2!.3!.3!) = 10
 I'm looking for a function to generate all the partitions using
Mathematica 3.0 .
I'm not sure, but I think the package Combinatorica doesn't have a
function to do this.
For example, I'm trying to think up a function f  like this one:

In[ ] = f [ {A,B,C,D,E,F},{3,3}]
Out [ ] = { { {A,B,C},{D,E,F} }, { {
A,B,F},{C,D,E}},...................} and so on.
In [ ] = Length[%]
Out [ ] = 10

Please, help me.
Thanks!

• Follow-Ups:
  • Re: Help on Partitions, Again!!!
    • From: "Carl K. Woll" <carlw@u.washington.edu>