报告题目：Long sequences having notwo nonempty zero-sum subsequences of distinct lengths

报告人：高维东教授（天津大学）

报告日期：2021/6/4 时间：14：00—15：00

报告地点：腾讯会议（线上）ID：317 904 535

报告摘要：Let $G$ be an additive finite abelian group. We say a sequence of elements (repetition allowed) from $G$ a {\sl zero-sum sequence} if the sum of all terms of $S$ equals to 0 (the identity element of $G$). In 2012, Girard posed a problem of determining the smallestpositive integer $t$, denoted by $\mathrm{disc}(G)$, such that everysequence $S$ over $G$ of length $|S|\geq t$ has two nonemptyzero-sum subsequences of distinct lengths. The study on problems related to $\mathrm{disc}(G)$ can track back to 1970's, Graham conjectured that if $p$ is a prime and $S$ isa sequence of length $|S|=p$ over $C_{p}$ such that all (nontrivial)zero-sum subsequences have the same length, then $S$ must contain atmost two distinct terms. In 1976, Erd\H{o}s and Szemer\'{e}di confirmed this conjecture for sufficiently large primes $p$. We will present some new results and open problems on $\mathrm{disc}(G)$.

报告人简介：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ErdÖs-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100多篇。