Re: Creating combinations from a group of sets

• To: mathgroup at smc.vnet.net
• Subject: [mg48703] Re: [mg48679] Creating combinations from a group of sets
• From: Adriano Pascoletti <pascolet at dimi.uniud.it>
• Date: Fri, 11 Jun 2004 03:52:26 -0400 (EDT)
• References: <200406100643.CAA29466@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Il giorno 10/giu/04, alle 08:43, Jeanette L Domber ha scritto:

>
> 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.

Hi,
use Outer[List, l1, l2,...,ln] followed by Flatten[...,n-1]

In[41]:=
Outer[List,{1,2,3},{4,5},{6},{7,8}]

Out[41]=
{{{{{1,4,6,7},{1,4,6,8}}},{{{1,5,6,7},{1,5,6,8}}}},{{{{2,4,6,7},{2,4,

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

In[43]:=
Flatten[%,3]

Out[43]=
{{1,4,6,7},{1,4,6,8},{1,5,6,7},{1,5,6,8},{2,4,6,7},{2,4,6,8},
{2,5,6,7},{2,5,6,8},{3,4,6,7},{3,4,6,8},{3,5,6,7},{3,5,6,8}}

A. Pascoletti

------------------------------------------------------------------------
--------