2022 Combinatorics Workshop

Intersective sets over abelian groups

30 Sept 2022, 14:30

20m

Contributed talk Session 1

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 $D_G(J,N)\le (p-1{)}^N$ 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 $J$.