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Largest 3-uniform set systems with VC-dimension 2
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Largest 3-uniform set systems with VC-dimension 2
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We determine the largest size of $3$-uniform set systems on $[n]$ with VC-dimension $2$ for all $n$.
Forward citations
Cited by 3 Pith papers
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A disproof of the uniform witness conjecture
Disproves the uniform witness conjecture via explicit construction of larger families than the bound binom(n-1,d) for d≥4 and ceil((d+2)/2)≤s≤d-1.
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Beating the Ahlswede--Khachatrian bound for the Erd\H{o}s--Frankl--Pach problem
New explicit constructions yield (d+1)-uniform VC-d families larger than the Ahlswede-Khachatrian size for d≥3, disproving the Mubayi-Zhao conjecture.
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Recursive Lifting Beyond the Ahlswede--Khachatrian Construction
For every d≥3 and n≥d+3, M_d(n) ≥ binom(n-1,d)+binom(n-4,d-2)+M_{d-3}(n-5), beating the Ahlswede–Khachatrian/Mubayi–Zhao lower bound via recursive lifting.
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