collaborators

9 papers

math.CO2026

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

Hong-Jun Ge, Zixiang Xu

A measurable set is called zero-sum-free if there are no with $\boldsymbol{x}+\boldsymbol{y}+\bolds…

math.CO2026

A disproof of the uniform witness conjecture

Zixiang Xu

The study of -uniform set systems with VC-dimension at most links the Erdős--Ko--Rado theorem with VC-dimension. But already in 1997, Ahlswede and Khachatrian showed th…

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 , every -uniform family on with VC-dimension has si…

math.CO2026

Balanced Sperner families via the topological Tverberg theorem

Chong Shangguan, Zixiang Xu, Yulin Yang

For every prime power , we show that any Sperner family with contains 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 with metric has cardinality when and when 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 with bounded symmetric difference. Liao, Liu and Yan recently established a vector-space analogue in t…