Zixiang Xu

collaborators

3 papers

math.CO2026

A disproof of the uniform witness conjecture

Zixiang Xu

The study of $(d + 1)$ -uniform set systems with VC-dimension at most $d$ links the Erdős--Ko--Rado theorem with VC-dimension. But already in 1997, Ahlswede and Khachatrian showed tha…

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…

A disproof of the uniform witness conjecture

Largest 3-uniform set systems with VC-dimension 2

Uniform set systems with small VC-dimension

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