Abel群上的逆零和问题

Zero-sum theory is one of the two branches of Combinatorial Number Theory, and is one of the research focus of Combinatorial Mathematics and Number Theory. The project is going to investigate the structure of two types of zero-sum sequences: (1) the conjecture on the structure of Normal sequence proposed by Weidong Gao; (2) the structure of a zero-sum free sequence over non- finite cyclic group with length more than the half of it's Davenport's constant. These problems have important theoretical significance and academic value.

零和理论是组合数论的两个重要分支之一，是当前组合数学与数论研究的热点之一。本项目拟研究两类零和序列的结构：(1)、进一步探索高维东提出的关于Normal sequence结构的猜想；(2)、研究非循环群上长度超过其Davenport常数的零和自由序列的结构问题。这些问题的研究有着重要的理论意义和学术价值。

零和理论是组合数论的主要研究内容，是当前组合数学与数论研究的热点之一，这些问题的研究有着重要的理论意义和学术价值。本课题研究了秩为2的非循环群上长度超过其Davenport常数的零和自由序列的结构问题, 得到了两个结果。