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A conjecture of Frankl proposed in the 1980s states that for n≥2d, every Sperner family F⊆ 2[n] of VC-dimension at most d has at most nd members. We prove this conjecture for every fixed d and large n, and show that equality holds only when F is [n]d or [n]n-d.
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Ge et al. (2026) studied this question.
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