Zixiang Xu

works on

canonical ramsey theory 1 colored transversal 1 combinatorial geometry 1 convex set unions 1 discrete geometry 1 euclidean ramsey theory 1 partition bounds 1 ramsey property 1 simplices 1 tverberg theorem 1

From the 2 of 14 linked papers with an AI index.

most citedSperner systems with restricted differences

1 citations · 1 across the 5 of their papers we have counts for

collaborators

14 papers

math.CO2026

Economical lattice coverings by determined segments

Gennian Ge, Yang Shu, Zixiang Xu

For fixed $d \geq 2$ , let $τ_{d} (n)$ be the minimum size of a set $S \subseteq {0, \dots, n}^{d}$ such that the affine lines determined by pairs of distinct points of $S$ cover the grid.…

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

Tverberg's theorem for unions of convex sets: Sharp bounds and colored extensions

Gennian Ge, Yang Shu, Zixiang Xu

The paper studies Tverberg-type partitions for point sets where each part is covered by a bounded number of convex sets, establishing asymptotically sharp lower and improved upper…

math.CO2026

All simplices exhibit canonical Ramsey property

Gennian Ge, Yang Shu, Zixiang Xu +1

The authors prove that every nondegenerate simplex possesses the canonical Ramsey property, settling a long‑standing open question in canonical Euclidean Ramsey theory and giving a…

math.CO2026★ 1 cited

Sperner systems with restricted differences

Zixiang Xu, Chi Hoi Yip

Let $F$ be a family of subsets of $[n]$ and $L$ be a subset of $[n]$ . We say $F$ is an $L$ -differencing Sperner system if $∣ A ∖ B ∣ \in L$ for any distinct…

math.CO2026

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…