Xiaochen Zhao

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5 papers · 1 filter

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 Erdős--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

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.CO2024

Algebraic approach to stability results for Erdős-Ko-Rado theorem

Gennian Ge, Zixiang Xu, Xiaochen Zhao

Celebrated results often unfold like episodes in a long-running series. In the field of extremal set thoery, Erdős, Ko, and Rado in 1961 established that any $k$ -uniform intersecti…