Every finite union-closed family other than has an element belonging to at least
(1)
of its members. The proof applies the binary entropy product inequality coordinate by coordinate to the union of two independent uniform members of the family.

Ancestors (8)

  1. Union-closed sets conjecture
  2. Union-closed family
  3. Set family
  4. Extremal set theory
  5. Combinatorics
  6. Area of mathematics
  7. Mathematics
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