union_closed.variants.yu

Specification

Yu [Yu23] showed that the union-closed sets conjecture holds with a constant of approximately 0.38234 instead of 1/2. [Yu23] Yu, Lei (2023). "Dimension-free bounds for the union-closed sets conjecture". Entropy. 25 (5): 767.

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Lean 4 Statement

theorem union_closed.variants.yu
    [Nonempty n]
    (h_ne_singleton_empty : A ≠ {∅})
    (h_union_closed : IsUnionClosed A) :
    ∃ i : n, (0.38234 : ℚ) * #A ≤ #{x ∈ A | i ∈ x}

ID: Wikipedia__UnionClosed__union_closed.variants.yu

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