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

Jian Wang , Zixiang Xu , Shengtong Zhang This is my paper · ORCID

classification math.CO

keywords largestsystemsuniformvc-dimensiondeterminesize

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abstract

We determine the largest size of $3$-uniform set systems on $[n]$ with VC-dimension $2$ for all $n$.

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Recursive Lifting Beyond the Ahlswede--Khachatrian Construction
math.CO 2026-07 accept novelty 6.5 of 10

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.