报告题目：On tiny zero-sum sequences over finite abelian groups

报告嘉宾：惠婉珍 博士 布鲁克大学

报告时间：2023年7月9日 09:00

腾讯会议ID：394 756 496

报告摘要：Let G be an additive finite abelian group. Let S be a sequence over G, and k(S) be its cross number. Let t(G) (resp. \eta(G)) be the smallest integer t such that every sequence of t elements, repetition allowed, from G has a non-empty zero-sum subsequence T with k(T)<=1 (resp. |T|<=exp(G)). It is easy to see that t(G)>=\eta(G). It is known that t(G)=\eta(G)=|G| when G is cyclic, and for any integer r>=3 there are infinitely many groups G of rank r such that t(G) > \eta(G). Girard (2012) conjectured that t(G)=\eta(G) for all finite abelian groups of rank 2. We confirm this conjecture for more groups, including the groups G=C_n \oplus C_n with the smallest prime divisor of n not less than the number of distinct prime divisors of n.

报告嘉宾简介：惠婉珍，2022年6月于南开大学获得博士学位，现于加拿大布鲁克大学做博士后，研究方向为组合数论，主要从直接问题和反问题两个方向对若干零和不变量及无零和序列的结构进行了研究。目前在J. Number Theory, Int. J. Number Theory, Acta Math. Hungar. 等SCI杂志发表论文近十篇，参与过天津市教委项目及国家自然科学基金面上项目等。