Gennian Ge

activity

20242026

most citedThe Frankl-Pach upper bound is not tight for any uniformity

1 citations · 1 across the 17 of their papers we have counts for

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17 papers · 1 filter

math.CO2026

The maximum $t$ -diversity of $t$ -intersecting families of permutations

Yuhang Cao, Gennian Ge, Jian Wang +2

The study of $t$ -intersecting families in symmetric groups received lots of attention in the last two decades. In this paper, we study two different kinds of stability results for…

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

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

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

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.CO2026

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 $q$ -ary alphabet. Let $Σ_{q}^{n}$ be the set of sequences…

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.CO2026

Monochromatic unit equilateral triangle on low-dimensional spheres

Xiaochen Zhao, Gennian Ge

A result of Matoušek and Rödl in 1995 states that for every $ε > 0$ and every triangle $T$ with circumradius $ρ (T)$ , there exists a dimension $n = n (ε, T)$ such that…

math.CO2026

Improvement on the Erdős-Kleitman conjecture via the KKL theorem

Gennian Ge, Jialuo Wang, Zixiang Xu

In 1974, Erdős and Kleitman conjectured that if a family $F \subseteq 2^{[n]}$ contains no matching of size $s$ and is maximal with respect to this property, then $ |\ma…

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

Progress towards generalized Nash-Williams' conjecture on $K_{4}$ -decompositions

Menglong Zhang, Gennian Ge

A $K_{4}$ -decomposition of a graph is a partition of its edges into $K_{4}$ s. A fractional $K_{4}$ -decomposition is an assignment of a nonnegative weight to each $K_{4}$ in a graph such th…

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…

math.CO2024★ 1 cited

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…

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…

The maximum t-diversity of t-intersecting families of permutations

Economical lattice coverings by determined segments

Largest Sperner families with restricted differences

All simplices exhibit canonical Ramsey property

Recursive Lifting Beyond the Ahlswede--Khachatrian Construction

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

Extremal Deletion-Ball Intersections under Run-Count and Lower-Order Deletion-Ball Intersection Constraints

Recursive lower bounds for uniform set systems of bounded VC-dimension

Universal Fourier-inertia bounds for prescribed even distances

Monochromatic unit equilateral triangle on low-dimensional spheres

Improvement on the Erdős-Kleitman conjecture via the KKL theorem

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

Canonical Ramsey: triangles, rectangles and beyond

Progress towards generalized Nash-Williams' conjecture on K4​-decompositions

All rectangles exhibit canonical Ramsey property

The Frankl-Pach upper bound is not tight for any uniformity

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

The maximum $t$ -diversity of $t$ -intersecting families of permutations

Progress towards generalized Nash-Williams' conjecture on $K_{4}$ -decompositions