Xiaochen Zhao

collaborators

6 papers

math.CO2026

Largest Sperner families with restricted differences

Gennian Ge, Zixiang Xu, Xiaochen Zhao

Let $L$ be a fixed set of positive integers. A family $F \subseteq 2^{[n]}$ is called $L$ -differencing if $∣ A ∖ B ∣ \in L$ for every ordered pair of distin…

math.CO2026

Recursive Lifting Beyond the Ahlswede--Khachatrian Construction

Xiaochen Zhao, Gennian Ge

For the ErdÅs--Frankl--Pach problem on uniform set systems of bounded VC-dimension, the Ahlswede--Khachatrian/Mubayi--Zhao construction has long served as the standard lower-bound…

math.CO2026

Recursive lower bounds for uniform set systems of bounded VC-dimension

Xiaochen Zhao, Gennian Ge

For integers $n \geq d + 1$ , let $M_{d} (n)$ denote the maximum size of a $(d + 1)$ -uniform family on an $n$ -element ground set with VC-dimension at most $d$ . For $n \geq 2 d + 2$ , the c…

math.CO2026★ 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.CO2026

Universal Fourier-inertia bounds for prescribed even distances

Xiaochen Zhao, Gennian Ge

The study of set families with restricted Hamming distances is a classical topic of extremal combinatorics and coding theory. Let $H=\{A\subseteq[n]: |A|\text{ is even}\}$ be the…

math.CO2026

Monochromatic unit equilateral triangle on low-dimensional spheres

Xiaochen Zhao, Gennian Ge

A result of MatouÅ¡ek and RÃ¶dl in 1995 states that for every $ε > 0$ and every triangle $T$ with circumradius $I ¨ (T)$ , there exists a dimension $n = n (ε, T)$ such t…