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Largest 3-uniform set systems with VC-dimension 2

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arxiv 2505.07756 v1 pith:AIQG2CIJ submitted 2025-05-12 math.CO

Largest 3-uniform set systems with VC-dimension 2

classification math.CO
keywords largestsystemsuniformvc-dimensiondeterminesize
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We determine the largest size of $3$-uniform set systems on $[n]$ with VC-dimension $2$ for all $n$.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. A disproof of the uniform witness conjecture

    math.CO 2026-06 unverdicted novelty 8.0

    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.

  2. Beating the Ahlswede--Khachatrian bound for the Erd\H{o}s--Frankl--Pach problem

    math.CO 2026-06 unverdicted novelty 8.0

    New explicit constructions yield (d+1)-uniform VC-d families larger than the Ahlswede-Khachatrian size for d≥3, disproving the Mubayi-Zhao conjecture.

  3. Recursive Lifting Beyond the Ahlswede--Khachatrian Construction

    math.CO 2026-07 accept novelty 6.5

    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.