An algorithm to find a tuple of subsets for which every subtuple of given size has union equal to the entire set

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This question involves the setup given here: Counting tuples of subsets for which every subtuple of a given size has union equal to the entire set
. Nonetheless this question is logically independent from the question asked there.



Problem: Determine an algorithm to find an element of $U^n_r,m,d$.



Potentially simplifying assumption: For given $mgeq d >0$, assume $n,r$ are chosen minimally so that $U^n_r,m,d neq 0$. This may or may not simplify the problem, I'm not sure.




combinatorics algorithms inclusion-exclusion




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    up vote
    0
    down vote

    favorite












    This question involves the setup given here: Counting tuples of subsets for which every subtuple of a given size has union equal to the entire set
    . Nonetheless this question is logically independent from the question asked there.



    Problem: Determine an algorithm to find an element of $U^n_r,m,d$.



    Potentially simplifying assumption: For given $mgeq d >0$, assume $n,r$ are chosen minimally so that $U^n_r,m,d neq 0$. This may or may not simplify the problem, I'm not sure.




    combinatorics algorithms inclusion-exclusion




    share|cite|improve this question





















      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      This question involves the setup given here: Counting tuples of subsets for which every subtuple of a given size has union equal to the entire set
      . Nonetheless this question is logically independent from the question asked there.



      Problem: Determine an algorithm to find an element of $U^n_r,m,d$.



      Potentially simplifying assumption: For given $mgeq d >0$, assume $n,r$ are chosen minimally so that $U^n_r,m,d neq 0$. This may or may not simplify the problem, I'm not sure.




      combinatorics algorithms inclusion-exclusion




      share|cite|improve this question











      This question involves the setup given here: Counting tuples of subsets for which every subtuple of a given size has union equal to the entire set
      . Nonetheless this question is logically independent from the question asked there.



      Problem: Determine an algorithm to find an element of $U^n_r,m,d$.



      Potentially simplifying assumption: For given $mgeq d >0$, assume $n,r$ are chosen minimally so that $U^n_r,m,d neq 0$. This may or may not simplify the problem, I'm not sure.





      combinatorics algorithms inclusion-exclusion





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      share|cite|improve this question




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      asked Aug 2 at 16:48









      Andrew

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