# Operations on sets of sets [duplicate]

How do I delete the duplicates of a set who's elements are themselves sets?

Here is an example: Deleting the duplicates from {{x,y},{y,x}} should give {{x,y}} (or {{y,x}}, both answers are equivalent).

I am particularly interested in the case when x and y are lists, but a solution that works for x and y of any type would be better.

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## marked as duplicate by Jens, Artes, R. M.♦, J. M.♦Jun 30 '12 at 1:17

Actually, the title should be: "Operations on lists of sets", as your example is not a set (though the outer list does contain sets). – István Zachar Jun 29 '12 at 19:37
@István The top and second level data structures have the same data type, so I think it should either be "...lists of lists" or "...sets of sets". I picked the latter to emphasize that I am thinking of them as sets even though the actual data type in Mathematica is a list. – Tyson Williams Jun 29 '12 at 19:43
It is not clear for me what are you expecting from deleting duplicates from {{2, 1}, {1, 2}, {3, 1}}. Should it be {{1, 2}, {1, 3}} or {1, 2, 3}? – István Zachar Jun 29 '12 at 19:44
This seems to be a duplicate of Pattern matching deletion of list items which itself was a duplicate of How can I remove B -> A from a list if A -> B is in the list. – Jens Jun 29 '12 at 20:34
This might answer your question, too: How to use Union on list of lists without sorting – Thies Heidecke Jun 29 '12 at 21:26

Does

DeleteDuplicates[Sort /@ {{2, 1}, {1, 2}}]


help?

Edit : ( Just try your data - Mathematica is cool, isn't it ? )

DeleteDuplicates[Sort /@ {{x, y}, {y, x}}]

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Sorry for the misleading example. I clarified the question and example to make it clear that the elements of the inner sets are not integers. – Tyson Williams Jun 29 '12 at 19:36
Just try it with your data. – user21 Jun 29 '12 at 19:45
Weird, I had tried it, but I thought it gave me the wrong answer. It is working now though, so thanks! – Tyson Williams Jun 29 '12 at 19:47
I see. I think the order of operations tricked me and it executed the Sort /@ part sooner than I wanted. Adding parentheses to force the correct order fixed that. – Tyson Williams Jun 29 '12 at 19:50
Glad you could figure it out. – user21 Jun 29 '12 at 19:51

Here is another solution based on Union and its option SameTest :

Union[{{x, y}, {y, x}}, SameTest -> (Union[#1] == Union[#2] &)]

{{x, y}}

Union[{{2, 1}, {1, 2}, {3, 1}}, SameTest -> (Union[#1] == Union[#2] &)]

{{1, 2}, {3, 1}}


In case of more nested lists I would use Flatten on appropriate level, e.g.

Union @ Flatten[{ {{2, 1}}, {{1, 2}} }, 2]

{1, 2}


where DeleteDuplicates[Sort /@ { {{2, 1}}, {{1, 2}} }] does not work if we don't use Flatten. However, this is not a general solution, one has to consider appropriate examples and work on case by case basis.

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Sorry for the misleading example. I clarified the question and example to make it clear that the elements of the inner sets are not integers. – Tyson Williams Jun 29 '12 at 19:38
Pardon me but this does not delete duplicate sets: deleting duplicates from {{2, 1}, {1, 2}, {3, 1}} should result in {{1,2}, {1,3}}, as those are the two distinct sets, but Union@Flatten[{{2, 1}, {1, 2}, {3, 1}}] returns {1, 2, 3}. – István Zachar Jun 29 '12 at 19:41
@TysonWilliams Does it satisfy your needs ? Otherwise, could you give an appropriate example ? – Artes Jun 29 '12 at 21:18
@IstvánZachar Thanks for reporting the problem. I updated the answer. If you see another problems, let me know about them. Nethertheless, I hope it is a good alternative to ruebenko's answer, which is not too general, either . – Artes Jun 29 '12 at 21:21
@Artes: Nice use of SameTest! – István Zachar Jun 29 '12 at 21:39