Yang Shu

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6 papers · 1 filter

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

All simplices exhibit canonical Ramsey property

Gennian Ge, Yang Shu, Zixiang Xu +1

We prove that all nondegenerate simplices have the canonical Ramsey property, thereby resolving a central open problem in canonical Euclidean Ramsey theory and providing a canonica…

math.CO2026

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

Gennian Ge, Yang Shu, Zixiang Xu

Let $f_{r} (d, s_{1}, \dots, s_{r})$ be the least $N$ such that every $N$ -point set $P \subseteq R^{d}$ has an $r$ -partition $P = P_{1} ⊔ \dots ⊔ P_{r}$ with the followin…

math.CO2025

A Tverberg-type problem of Kalai: Two negative answers to questions of Alon and Smorodinsky, and the power of disjointness

Wenchong Chen, Gennian Ge, Yang Shu +2

Let $f_{r} (d, s_{1}, \dots, s_{r})$ denote the least integer $n$ such that every $n$ -point set $P \subseteq R^{d}$ admits a partition $P = P_{1} \cup \dots \cup P_{r}$ with the property that…

math.CO2025

Canonical Ramsey: triangles, rectangles and beyond

Yijia Fang, Gennian Ge, Yang Shu +3

In a seminal work, Cheng and Xu showed that if $S$ is a square or a triangle with a certain property, then for every positive integer $r$ there exists $n_{0} (S)$ independent of $r$ s…

math.CO2025

All rectangles exhibit canonical Ramsey property

Gennian Ge, Yang Shu, Zixiang Xu

In a seminal work, Cheng and Xu proved that for any positive integer $r$, there exists an integer $n_0$, independent of $r$, such that every $r$-coloring of the $n$-dimen…