Chengfei Xie

activity

20202026

collaborators

11 papers

math.MG2026

On the weighted hard-core model and Rado's covering problem for congruent Euclidean balls

Chengfei Xie, Gennian Ge

Let $K$ be a symmetric convex body in $R^{d}$ and let $f (K)$ denote the largest constant $c$ such that every finite collection of translates of $K$ contains a pairwise disjo…

cs.IT2026

New bounds for covering codes under insertions or deletions

Chengfei Xie, Yubo Sun, Gennian Ge

Covering codes for insertions and deletions arise naturally in the study of synchronization errors and differ substantially from their classical counterparts in the Hamming metric.…

math.CO2025

Dot-product graphs in finite fields

Chengfei Xie, Gennian Ge

In this paper, we study the dot-product graphs in $F_{q}^{d}$ . We prove that if the size of the product of two adjacent sets is large enough, then the set of dot-product graph…

math.CO2023

Some results on similar configurations in subsets of $F_{q}^{d}$

Chengfei Xie, Gennian Ge

In this paper, we study problems about the similar configurations in $F_{q}^{d}$ . Let $G = (V, E)$ be a graph, where $V = {1, 2, \dots, n}$ and $E \subseteq (2 V)$ . For a s…

math.MG2022

On the lower bound for kissing numbers of $ℓ_{p}$ -spheres in high dimensions

Chengfei Xie, Gennian Ge

In this paper, we give some new lower bounds for the kissing number of $ℓ_{p}$ -spheres. These results improve the previous work due to Xu (2007). Our method is based on coding the…

cs.IT2022

Covering Grassmannian Codes: Bounds and Constructions

Bingchen Qian, Xin Wang, Chengfei Xie +1

Grassmannian $G_{q} (n, k)$ is the set of all $k$ -dimensional subspaces of the vector space $F_{q}^{n} .$ Recently, Etzion and Zhang introduced a new notion called coveri…

math.MG2022

On the lower bound for packing densities of superballs in high dimensions

Chengfei Xie, Gennian Ge

Define the superball with radius $r$ and center $0$ in $R^{n}$ to be the set $$ \left\{{\boldsymbol x}\in\mathbb{R}^n:\sum_{j=1}^{m}\left(x_{k_j+1}^2+x_{k_j+2}…

math.CO2021

Some sum-product estimates in matrix rings over finite fields

Chengfei Xie, Gennian Ge

We study some sum-product problems over matrix rings. Firstly, for $A, B, C \subseteq M_{n} (F_{q})$ , we have $∣ A + B C ∣ ≳ q^{n^{2}},$ whenever $|A||B||C|\gtrsim q^{3n^2-\fr…

math.CO2021

On the minimal degree condition of graphs implying some properties of subgraphs

Bingchen Qian, Chengfei Xie, Gennian Ge

Erdős posed the problem of finding conditions on a graph $G$ that imply the largest number of edges in a triangle-free subgraph is equal to the largest number of edges in a biparti…

math.CO2021

Some Results on $k$ -Turán-good Graphs

Bingchen Qian, Chengfei Xie, Gennian Ge

For a graph $H$ and a $k$ -chromatic graph $F,$ if the Turán graph $T_{k - 1} (n)$ has the maximum number of copies of $H$ among all $n$ -vertex $F$ -free graphs (for $n$ large enough),…

math.CO2020

On the size of Nikodym sets in spaces over rings

Chengfei Xie, Gennian Ge

A Nikodym set $N \subseteq (Z / (N Z))^{n}$ is a set containing $L ∖ {x}$ for every $x \in (Z / (N Z))^{n}$ , where $L$ is a line passing thr…

On the weighted hard-core model and Rado's covering problem for congruent Euclidean balls

New bounds for covering codes under insertions or deletions

Dot-product graphs in finite fields

Some results on similar configurations in subsets of Fqd​

On the lower bound for kissing numbers of ℓp​-spheres in high dimensions

Covering Grassmannian Codes: Bounds and Constructions

On the lower bound for packing densities of superballs in high dimensions

Some sum-product estimates in matrix rings over finite fields

On the minimal degree condition of graphs implying some properties of subgraphs

Some Results on k-Turán-good Graphs

On the size of Nikodym sets in spaces over rings

Some results on similar configurations in subsets of $F_{q}^{d}$

On the lower bound for kissing numbers of $ℓ_{p}$ -spheres in high dimensions

Some Results on $k$ -Turán-good Graphs