报告摘要:Let $G$ be an additive finite abelian group. Let$S=(g_1, ..., g_k)$ be a sequence over $G$. Let$\sigma(S)=\sum_{i=1}^k g_i\in G$. The sequence $S$ is called a zero-sum sequence if $\sigma(S)=0$. Let $D(G)$ denote the Davenport constant of $G$, which is defined as thesmallest integer $t$ such that every sequence $S$ over $G$ of length $|S|\ge t$ contains a nonempty zero-sum subsequence. The problem of determining $D(G)$ was proposed by H. Davenport in 1966, and he also pointed out that $D(G)$ is connected to the algebraic number theory in the following way. Let $K$ be an algebraic number field and let $G$ be its class group. Then $D(G)$ is the maximal number of the prime ideals (counting multiplicity) that can occur in the decomposition of an irreducible integer in $K$. So it plays an important role in the factorization theory in the algebraic number theory. Furthermore, the Davenport's constant is also connected with the graph theory, the classical number theory and the coding theory, and the study of $D(G)$ has attracted a great deal of attention. In this talk, we will present some results and open problems on $D(G)$.

专家简介:高维东教授现就职于天津大学应用数学中心。他1994年从四川大学获得博士学位,导师为孙琦教授。1994-1998年他先后于大连理工大学应用数学系和奥地利格拉茨大学数学系从事博士后研究。他的主要研究兴趣在组合数论中的零和理论,1996年他建立了两个著名组合课题Davenport常数和Erdos-Ginzburg-Ziv定理之间的基本联系,从而将这两个原被各自独立研究的课题统一起来。这一结论被同行在公开发表的论文和评论中称为基础性结果(a fundamental result)和漂亮(beautiful)的结果,并指出其已众所周知(well known)。目前已发表学术论文110多篇。