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Creating combinations from a group of sets

• To: mathgroup at smc.vnet.net
• Subject: [mg48679] Creating combinations from a group of sets
• From: Jeanette L Domber <Jeanette.L.Domber at aero.org>
• Date: Thu, 10 Jun 2004 02:43:30 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

I have a group of sets:

{1,2,3}
{4,5}
{6}
{7,8}

I wish to create all unique combinations of the sets that contain exactly one element from each set:

{1,4,6,7}
{1,5,6,7}
{1,4,6,8}
{1,5,6,8}
{2,4,6,7}
{2,5,6,7}
etc.

In all, there should be 12 combinations.

If I use KSubsets giving it a list {1,2,3,4,5,6,7,8} to create combinations containing 4 elements, I get a list of 70 combinations, 58 of which are extraneous to my application.

Does anyone know how to manipulate the functions in DiscreteMath`Combinatorica` to accomplish this efficiently?

Thanks,
    Jeanette

• Follow-Ups:
  • Re: Creating combinations from a group of sets
    • From: János <janos.lobb@yale.edu>
  • Re: Creating combinations from a group of sets
    • From: DrBob <drbob@bigfoot.com>
  • Re: Creating combinations from a group of sets
    • From: Adriano Pascoletti <pascolet@dimi.uniud.it>