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Any ideas on expanded results for SetPartitions in discrete-combinatoria


Looking for suggestions...

SetPartitions drops partitions that have "overlaps", any ideas on how to 
modify or recreate a SetPartitions function that doesn't drop these?

For example

SetPartitions[{A,B,C}]

Generates:


{{{A, B, C}}, {{A}, {B, C}}, {{A, B}, {C}}, {{A, C}, {B}}, {{A}, {B}, {C}}}


What it is missing (for my needs) are the following:

{{A,B}, {B, C}}, {{A,C}, {B, C}}, {{A,B}, {A, C}}, {{A,B}, {B, C},{A,C}}

I have tried doing this:

SetPartitions[{A,A,B,B,C,C}] which adds them but then I need a quick way 
to delete the subsets that have duplicate elemenets.


Either way will get me where I need to be. But I can not figure it out.
   
Thanks in advance for any help.

Ike
wde at pdx.edu


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