Zixiang Xu

collaborators

9 papers

math.CO2026

The sharp asymptotic density of zero-sum-free spherical sets

Hong-Jun Ge, Zixiang Xu

A measurable set $A \subseteq S^{d - 1}$ is called zero-sum-free if there are no $x, y, z \in A$ with $\boldsymbol{x}+\boldsymbol{y}+\bolds…

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.CO2026

Beating the Ahlswede--Khachatrian bound for the Erdős--Frankl--Pach problem

Tuan Tran, Zixiang Xu

In the 1980s, Erdős and, independently, Frankl and Pach conjectured that, for sufficiently large $n$ , every $(d + 1)$ -uniform family on ${1, \dots, n}$ with VC-dimension $d$ has siz…

math.CO2026

Balanced Sperner families via the topological Tverberg theorem

Chong Shangguan, Zixiang Xu, Yulin Yang

For every prime power $r \geq 2$ , we show that any Sperner family $F \subseteq 2^{[n]}$ with $∣ F ∣ \geq (r - 1) n + 1$ contains $r$ pairwise disjoint nonempty subfamilies wh…

math.CO2026

Kusner's conjecture: Exact values and linear bounds

Hong-Jun Ge, Zixiang Xu, Yang Zhou

In 1983, Kusner conjectured that the largest equilateral set in $R^{n}$ with metric $ℓ_{p}$ has cardinality $n + 1$ when $1 < p < \infty$ and $2 n$ when $p = 1.$ This conjecture…

math.CO2026

Kleitman's theorem over vector spaces: parity phenomena in canonical and global stability

Chenhui Lv, Zixiang Xu

In 1966, Kleitman determined the maximum size of a family of subsets of $[n]$ with bounded symmetric difference. Liao, Liu and Yan recently established a vector-space analogue in t…

math.CO2026

A solution to a strengthened conjecture of Bukh, van Hintum and Keevash on additive bases

Zixiang Xu

Motivated by the change-of-domain problem for additive bases, Bukh, van Hintum and Keevash conjectured that if $A,B\subseteq \mathbb{Q}^{n}$ and \(\{\boldsymbol{e}_i+\boldsymbol{…

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…

The sharp asymptotic density of zero-sum-free spherical sets

A disproof of the uniform witness conjecture

Beating the Ahlswede--Khachatrian bound for the Erdős--Frankl--Pach problem

Balanced Sperner families via the topological Tverberg theorem

Kusner's conjecture: Exact values and linear bounds

Kleitman's theorem over vector spaces: parity phenomena in canonical and global stability

A solution to a strengthened conjecture of Bukh, van Hintum and Keevash on additive bases

Largest 3-uniform set systems with VC-dimension 2

Uniform set systems with small VC-dimension

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