3
$\begingroup$

I have the following list:

i=2
k=3
 list = Tuples[Tuples[{0, 1}, i], k]

{{{0, 0}, {0, 0}, {0, 0}}, {{0, 0}, {0, 0}, {0, 1}}, {{0, 0}, {0, 0}, {1, 0}}, {{0, 0}, {0, 0}, {1, 1}}, {{0, 0}, {0, 1}, {0,0}}, {{0, 0}, {0, 1}, {0, 1}}, {{0, 0}, {0, 1}, {1, 0}}, {{0, 0}, {0, 1}, {1, 1}}, {{0, 0}, {1, 0}, {0, 0}}, {{0, 0}, {1, 0}, {0, 1}}, {{0, 0}, {1, 0}, {1, 0}}, {{0, 0}, {1, 0}, {1, 1}}, {{0, 0}, {1, 1}, {0, 0}}, {{0, 0}, {1, 1}, {0, 1}}, {{0, 0}, {1, 1}, {1, 0}}, {{0, 0}, {1, 1}, {1, 1}}, {{0, 1}, {0, 0}, {0, 0}}, {{0, 1}, {0, 0}, {0, 1}}, {{0, 1}, {0, 0}, {1, 0}}, {{0, 1}, {0, 0}, {1, 1}}, {{0, 1}, {0, 1}, {0, 0}}, {{0, 1}, {0, 1}, {0, 1}}, {{0, 1}, {0, 1}, {1, 0}}, {{0, 1}, {0, 1}, {1, 1}}, {{0, 1}, {1, 0}, {0, 0}}, {{0, 1}, {1, 0}, {0, 1}}, {{0, 1}, {1, 0}, {1, 0}}, {{0, 1}, {1, 0}, {1, 1}}, {{0, 1}, {1, 1}, {0, 0}}, {{0, 1}, {1, 1}, {0, 1}}, {{0, 1}, {1, 1}, {1, 0}}, {{0, 1}, {1, 1}, {1, 1}}, {{1, 0}, {0, 0}, {0, 0}}, {{1, 0}, {0, 0}, {0, 1}}, {{1, 0}, {0, 0}, {1, 0}}, {{1, 0}, {0, 0}, {1, 1}}, {{1, 0}, {0, 1}, {0, 0}}, {{1, 0}, {0, 1}, {0, 1}}, {{1, 0}, {0, 1}, {1, 0}}, {{1, 0}, {0, 1}, {1, 1}}, {{1, 0}, {1, 0}, {0, 0}}, {{1, 0}, {1, 0}, {0, 1}}, {{1, 0}, {1, 0}, {1, 0}}, {{1, 0}, {1, 0}, {1, 1}}, {{1, 0}, {1, 1}, {0, 0}}, {{1, 0}, {1, 1}, {0, 1}}, {{1, 0}, {1, 1}, {1, 0}}, {{1, 0}, {1, 1}, {1, 1}}, {{1, 1}, {0, 0}, {0, 0}}, {{1, 1}, {0, 0}, {0, 1}}, {{1, 1}, {0, 0}, {1, 0}}, {{1, 1}, {0, 0}, {1, 1}}, {{1, 1}, {0, 1}, {0, 0}}, {{1, 1}, {0, 1}, {0, 1}}, {{1, 1}, {0, 1}, {1, 0}}, {{1, 1}, {0, 1}, {1, 1}}, {{1, 1}, {1, 0}, {0, 0}}, {{1, 1}, {1, 0}, {0, 1}}, {{1, 1}, {1, 0}, {1, 0}}, {{1, 1}, {1, 0}, {1, 1}}, {{1, 1}, {1, 1}, {0, 0}}, {{1, 1}, {1, 1}, {0, 1}}, {{1, 1}, {1, 1}, {1, 0}}, {{1, 1}, {1, 1}, {1, 1}}}

I would like to remove redundant element, like "{{0, 1}, {0, 0}, {0, 0}}" since they have the same value like "{{1, 0}, {0, 0}, {0, 0}}". The "{{0, 0}, {0, 0}, {0, 0}}" element should be removed as well. Elements like "{{1, 1}, {0, 0}, {0, 0}}" are not equal to "{{0, 0}, {1, 1}, {0, 0}}" though. Note that the inner subsets are of size $i$ which are elements in subsets of size $k$.

Maybe the list should be created differently? How can I make this happen? The goal is to get it for any $i$ and $k$ in general.

For example, instead of

list = Tuples[Tuples[{0, 1}, 2], 2]
{{{0, 0}, {0, 0}}, {{0, 0}, {0, 1}}, {{0, 0}, {1, 0}}, {{0, 0}, {1, 
   1}}, {{0, 1}, {0, 0}}, {{0, 1}, {0, 1}}, {{0, 1}, {1, 0}}, {{0, 
   1}, {1, 1}}, {{1, 0}, {0, 0}}, {{1, 0}, {0, 1}}, {{1, 0}, {1, 
   0}}, {{1, 0}, {1, 1}}, {{1, 1}, {0, 0}}, {{1, 1}, {0, 1}}, {{1, 
   1}, {1, 0}}, {{1, 1}, {1, 1}}}  

a possible output is:

{{{0, 0}, {1, 0}}, {{0, 0}, {1, 1}}, {{1, 0}, {0, 0}}, {{1, 0}, {1, 
   0}}, {{1, 0}, {1, 1}}, {{1, 1}, {0, 0}}, {{1, 1}, {1, 0}}, {{1, 
   1}, {1, 1}}}
$\endgroup$
2
  • 1
    $\begingroup$ Please show your desired output. $\endgroup$ Jul 25, 2020 at 19:37
  • $\begingroup$ @PaulCommentary added an example, thanks. $\endgroup$
    – Y.L
    Jul 25, 2020 at 19:46

1 Answer 1

4
$\begingroup$
With[{i = 2, k = 3},
 DeleteCases[
  Tuples[DeleteDuplicatesBy[Tuples[{0, 1}, i], Sort], k],
  ConstantArray[0, {k, i}]
 ]]

Result:

{{{0, 0}, {0, 0}, {0, 1}}, {{0, 0}, {0, 0}, {1, 1}}, {{0, 0}, {0, 
   1}, {0, 0}}, {{0, 0}, {0, 1}, {0, 1}}, {{0, 0}, {0, 1}, {1, 
   1}}, {{0, 0}, {1, 1}, {0, 0}}, {{0, 0}, {1, 1}, {0, 1}}, {{0, 
   0}, {1, 1}, {1, 1}}, {{0, 1}, {0, 0}, {0, 0}}, {{0, 1}, {0, 0}, {0,
    1}}, {{0, 1}, {0, 0}, {1, 1}}, {{0, 1}, {0, 1}, {0, 0}}, {{0, 
   1}, {0, 1}, {0, 1}}, {{0, 1}, {0, 1}, {1, 1}}, {{0, 1}, {1, 1}, {0,
    0}}, {{0, 1}, {1, 1}, {0, 1}}, {{0, 1}, {1, 1}, {1, 1}}, {{1, 
   1}, {0, 0}, {0, 0}}, {{1, 1}, {0, 0}, {0, 1}}, {{1, 1}, {0, 0}, {1,
    1}}, {{1, 1}, {0, 1}, {0, 0}}, {{1, 1}, {0, 1}, {0, 1}}, {{1, 
   1}, {0, 1}, {1, 1}}, {{1, 1}, {1, 1}, {0, 0}}, {{1, 1}, {1, 1}, {0,
    1}}, {{1, 1}, {1, 1}, {1, 1}}}

For the 2,2 case, the result is:

{{{0, 0}, {0, 1}}, {{0, 0}, {1, 1}}, {{0, 1}, {0, 0}}, {{0, 1}, {0, 
   1}}, {{0, 1}, {1, 1}}, {{1, 1}, {0, 0}}, {{1, 1}, {0, 1}}, {{1, 
   1}, {1, 1}}}

... which is the same as your expected output, if you're willing to apply Map[Sort,expected,{2}] to change {1,0} into {0,1}

$\endgroup$
3
  • $\begingroup$ Beautiful @flinty, just how do I apply the Map[Sort,expected,{2}] is I need to? Thank you! $\endgroup$
    – Y.L
    Jul 25, 2020 at 20:53
  • $\begingroup$ What do you mean? I only put that in in case you're worried about the order in each sub-sub-list. You could do Map[Reverse,result,{2}] if you want the results in the same order too. $\endgroup$
    – flinty
    Jul 25, 2020 at 20:54
  • $\begingroup$ The "Reverse" fixed it. Thank you so much. $\endgroup$
    – Y.L
    Jul 25, 2020 at 20:57

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