Inverse zero-sum problems II
Inverse zero-sum problems II
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DOI：
10.4064/aa143-4-2
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发表时间：
2008-01
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通讯作者：
W. Schmid
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文献类型：
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作者：
W. Schmid
设G是可加有限交换群.如果$G$上的序列的各项之和为零并且没有合适的子序列具有此性质，则该序列称为最小零和序列。达文波特常数$G$是G$上最小零和序列长度的最大值。它的价值是众所周知的群秩二。研究了秩为2的群的最大长度的极小零和序列的结构。假设一个很好的支持猜想这个问题的形式$C_m \oplus C_m$的群体，我们确定这些序列的结构，为两个群体的秩。结合我们的结果和部分结果，这个猜想，产生无条件的结果，某些群体的秩二。
Let $G$ be an additive finite abelian group. A sequence over $G$ is called a minimal zero-sum sequence if the sum of its terms is zero and no proper subsequence has this property. Davenport's constant of $G$ is the maximum of the lengths of the minimal zero-sum sequences over $G$. Its value is well-known for groups of rank two. We investigate the structure of minimal zero-sum sequences of maximal length for groups of rank two. Assuming a well-supported conjecture on this problem for groups of the form $C_m \oplus C_m$, we determine the structure of these sequences for groups of rank two. Combining our result and partial results on this conjecture, yields unconditional results for certain groups of rank two.