本项目的研究内容属于组合数论和分解理论的范畴。令G为一个有限Abel群，令S为群G上的一个有限序列，如果S的所有项之和为零，则称S为零和序列。典型的零和问题研究的是在什么样的条件下，给定的序列中含有非空的满足特定要求的零和子列。本项目拟研究组合零和常数cross number和tiny零和序列相关的问题。在19世纪，人们发现代数整数环并不是唯一分解的，从那时起人们开始关注如何刻画代数整数环的非唯一分解的现象。如果我们以B(G)来记群G上的所有零和序列构成的集合，以序列的拼接作为B(G)上的运算，那B(G)则构成了一个半群。通过建立Krull monoid H(如代数整数环)到B(G)的传递同态，研究H的非唯一分解现象可以通过研究B(G)上的算术零和常数来实现，由于这一理论主要使用组合数论的工具和方法，通常称为组合分解理论。本项目拟研究算术零和常数中与分解长度和分解距离等相关的问题。

The proposed project lies in the combinatorial number theory and the factorization theory. Let G be a finite abelian group and let S be a finite sequence over G. If the sum of all the terms of S equals zero, then S is called a zero-sum sequence over G. A typical zero-sum problem studies conditions which ensure that given sequences have non-empty zero-sum subsequences with prescribed properties.In this project, we will study the direct and inverse problems concerning the cross number and tiny zero-sum sequences..It was an important observation of mathematicians of the 19th century that in general the ring of integers of an algebraic number field is not factorial. Since then, people began to characterize the various phenomena of non-uniqueness of factorizations of the ring of integers. Let B(G) denote the set of all zero-sum sequences over G and let the concatenation be the operation of B(G). Then B(G) is a semigroup. To study the phenomena of non-uniqueness of a Krull monoid H (for example, the ring of integers), we could study the arithmetic of B(G) by building a transfer homomorphism from H to B(G). The study of the factorizations of B(G) is always called combinatorial factorization theory, since the tools and the methods are mainly from combinatorial number theory. In this project, we will study the arithmetic zero-sum invariants concerning the sets of lengths and the set of distances and others.