【数学学院】Additive Bases in Abelian Groups and Regular Sequences

报告人：高维东 教授，博士生导师 (南开大学组合数学中心， LPMC-TJKLC)

时间：2018年11月22日（周四）16:00-17:00

地点：四川大学数学学院西303学术报告厅

摘要：Let $G$ be a finite additive abelian group, and let $S$ be a sequence of elements from

$G$ (repetition allowed). We say that $S$ forms an additive basis of $G$ if every element of

$G$ can be expressed as the sum over a nonempty subsequence of $S$. We say that $S$ is

regular if for every proper subgroup $H\subseteq G$, $S$ has at most $|H|-1$ terms from $H$.

Let $\mathsf c_0(G)$ be the smallest integer $t$ such that every regular sequence $S$ over

$G$ of length $|S|\geq t$ forms an additive basis of $G$. We present some recent results on

$\mathsf c_0(G)$ and raise some related open problems.