Speaker
Zixiang Xu
(IBS ECOPRO)
Description
Given a finite abelian group $G$ and a subset $J\subset G$ with $0\in J$, let $D_{G}(J,N)$ be the maximum size of $A\subset G^{N}$ such that the difference set $A-A$ and $J^{N}$ have no non-trivial intersection. Recently, this extremal problem has been studied for different groups $G$ and subsets $J$. For example, using the linear algebra methods, Alon showed the upper bound $D_{G}(J,N)\leq (p-1)^{N}$ when $G=\mathbb{F}_{p}$ and $J=\{0,1\}^{N}$. In this talk, I will introduce some improved upper bounds of $D_{G}(J,N)$ for several groups $G$ and subsets $J$.
Primary authors
Mr
Chi Hoi Yip
Zixiang Xu
(IBS ECOPRO)
