3 papers
math.MG2026
On the weighted hard-core model and Rado's covering problem for congruent Euclidean balls
Chengfei Xie, Gennian Ge
Let denote the Euclidean unit ball in and denote the largest constant such that every finite collection of congruent Euclidean balls contains a pa…
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 . We prove that if the size of the product of two adjacent sets is large enough, then the set of dot-product graph…