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Wolfram Language

Eliminating duplicate pairings in permutation-based partitions

Jim Clinton

Posted 2 days ago

Union[Map[Sort, TakeList[#, {2, 2}] & /@ Permutations@Range@4, {2}]] Running the above code yields the following result: {{{1, 2}, {3, 4}}, {{1, 3}, {2, 4}}, {{1, 4}, {2, 3}}, {{2, 3}, {1, 4}}, {{2, 4}, {1, 3}}, {{3, 4}, {1, 2}}} How can I add/modify the code to further obtain the desired result as follows? {{{1, 2}, {3, 4}}, {{1, 3}, {2, 4}}, {{1, 4}, {2, 3}}}

Union[Map[Sort, TakeList[#, {2, 2}] & /@ Permutations@Range@4, {2}]]

Running the above code yields the following result:

{{{1, 2}, {3, 4}}, {{1, 3}, {2, 4}}, {{1, 4}, {2, 3}}, {{2, 3}, {1, 
   4}}, {{2, 4}, {1, 3}}, {{3, 4}, {1, 2}}}

How can I add/modify the code to further obtain the desired result as follows?

{{{1, 2}, {3, 4}}, {{1, 3}, {2, 4}}, {{1, 4}, {2, 3}}}

POSTED BY: Jim Clinton

3 Replies

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Hans Milton

Posted 1 day ago

You could use `DeleteDuplicatesBy` pairs=Union[Map[Sort,TakeList[#,{2,2}]&/@Permutations@Range@4,{2}]]; DeleteDuplicatesBy[pairs,Sort] (* {{{1,2},{3,4}},{{1,3},{2,4}},{{1,4},{2,3}}} *) With the operator form of `DeleteDuplicatesBy` Union[Map[Sort,TakeList[#,{2,2}]&/@Permutations@Range@4,{2}]]//DeleteDuplicatesBy[Sort]

You could use DeleteDuplicatesBy

pairs=Union[Map[Sort,TakeList[#,{2,2}]&/@Permutations@Range@4,{2}]];
DeleteDuplicatesBy[pairs,Sort]
(* {{{1,2},{3,4}},{{1,3},{2,4}},{{1,4},{2,3}}} *)

With the operator form of DeleteDuplicatesBy

Union[Map[Sort,TakeList[#,{2,2}]&/@Permutations@Range@4,{2}]]//DeleteDuplicatesBy[Sort]

POSTED BY: Hans Milton

Eric Rimbey

Posted 2 days ago

You could do something like this: DeleteDuplicates[ Permutations@Range@4, ContainsAll[#1[[1 ;; 2]], #2[[1 ;; 2]]] \|\| ContainsNone[#1[[1 ;; 2]], #2[[1 ;; 2]]] &] (* {{1, 2, 3, 4}, {1, 3, 2, 4}, {1, 4, 2, 3}} *) Then you can use `TakeList` or whatever to reshape into pairs of pairs.

POSTED BY: Eric Rimbey

Jim Clinton

Posted 2 days ago

Thanks for your help！ DeleteDuplicates[Permutations@Range@4, ContainsAll[#1[[1 ;; 2]], #2[[1 ;; 2]]] \|\| ContainsNone[#1[[1 ;; 2]], #2[[1 ;; 2]]] &] TakeList[#, {2, 2}] & /@ % Or DeleteDuplicates[Permutations@Range@4, ContainsAll[#1[[1 ;; 2]], #2[[1 ;; 2]]] \|\| ContainsNone[#1[[1 ;; 2]], #2[[1 ;; 2]]] &] Partition[#, 2] & /@ %

Thanks for your help！

DeleteDuplicates[Permutations@Range@4, 
 ContainsAll[#1[[1 ;; 2]], #2[[1 ;; 2]]] || 
   ContainsNone[#1[[1 ;; 2]], #2[[1 ;; 2]]] &]
TakeList[#, {2, 2}] & /@ %

DeleteDuplicates[Permutations@Range@4, 
 ContainsAll[#1[[1 ;; 2]], #2[[1 ;; 2]]] || 
   ContainsNone[#1[[1 ;; 2]], #2[[1 ;; 2]]] &]
Partition[#, 2] & /@ %

POSTED BY: Jim Clinton

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