Shengtong Zhang

most citedThe Frankl-Pach upper bound is not tight for any uniformity

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math.CO2025

Largest $3$ -uniform set systems with VC-dimension $2$

Jian Wang, Zixiang Xu, Shengtong Zhang

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

math.CO2025

Uniform set systems with small VC-dimension

Ting-Wei Chao, Zixiang Xu, Chi Hoi Yip +1

We investigate the longstanding problem of determining the maximum size of a $(d + 1)$ -uniform set system with VC-dimension at most $d$ . Since the seminal 1984 work of Frankl and Pac…

math.CO2024★ 1 cited

The Frankl-Pach upper bound is not tight for any uniformity

Gennian Ge, Zixiang Xu, Chi Hoi Yip +2

For any positive integers $n \geq d + 1 \geq 3$ , what is the maximum size of a $(d + 1)$ -uniform set system in $[n]$ with VC-dimension at most $d$ ? In 1984, Frankl and Pach initiated the s…

math.CO2024

Conic programming to understand sums of squares of eigenvalues of graphs

Gabriel Coutinho, Thomás Jung Spier, Shengtong Zhang

In this paper we prove a conjecture by Wocjan, Elphick and Anekstein (2018) which upper bounds the sum of the squares of the positive (or negative) eigenvalues of the adjacency mat…

Largest 3-uniform set systems with VC-dimension 2

Uniform set systems with small VC-dimension

The Frankl-Pach upper bound is not tight for any uniformity

Conic programming to understand sums of squares of eigenvalues of graphs

Largest $3$ -uniform set systems with VC-dimension $2$