Improves the Frankl–Pach upper bound on maximum size of (d+1)-uniform VC-dimension-d families to binom(n-1,d) + O_d(n^{d-1-1/(4d-2)}), disproves the Erdős–Frankl–Pach conjecture, and proposes a refined version.
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Uniform set systems with small VC-dimension
Improves the Frankl–Pach upper bound on maximum size of (d+1)-uniform VC-dimension-d families to binom(n-1,d) + O_d(n^{d-1-1/(4d-2)}), disproves the Erdős–Frankl–Pach conjecture, and proposes a refined version.