From the 2 of 6 linked papers with an AI index.
6 papers
Economical lattice coverings by determined segments
Gennian Ge, Yang Shu, Zixiang Xu
For fixed , let be the minimum size of a set such that the affine lines determined by pairs of distinct points of cover the grid.…
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…
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…
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 denote the least integer such that every -point set admits a partition with the property that…
Canonical Ramsey: triangles, rectangles and beyond
Yijia Fang, Gennian Ge, Yang Shu +3
In a seminal work, Cheng and Xu showed that if is a square or a triangle with a certain property, then for every positive integer there exists independent of s…
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…