From the 2 of 16 linked papers with an AI index.
16 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.…
Largest Sperner families with restricted differences
Gennian Ge, Zixiang Xu, Xiaochen Zhao
Let be a fixed set of positive integers. A family is called -differencing if for every ordered pair of distin…
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…
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…
Extremal Deletion-Ball Intersections under Run-Count and Lower-Order Deletion-Ball Intersection Constraints
Yubo Sun, Gennian Ge
Motivated by sequence reconstruction and reconstruction codes, we study extremal intersections of deletion balls over a fixed -ary alphabet. Let be the set of sequences…