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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math.CO 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
New explicit constructions yield (d+1)-uniform VC-d families larger than the Ahlswede-Khachatrian size for d≥3, disproving the Mubayi-Zhao conjecture.
citing papers explorer
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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.