关于经典零和不变量
On a classical zero-sum invariant
AI总结：
研究20世纪60年代零和理论中引入的有限阿贝尔群的经典零和不变量ν(G)，明确其为满足特定子序列和性质的最小整数ℓ。
AI中文摘要：
设G为非平凡有限阿贝尔群，ν(G)是最小整数ℓ，使得G上长度至少为ℓ的每个零和自由序列T满足：所有未作为T的子序列和出现的G非零元素，都属于G某子群的一个真陪集。我们研究该不变量ν(G)，它是20世纪60年代《零和理论》中引入的。
英文摘要：
Let $G$ be a nontrivial, finite abelian group. Then $ν(G)$ is the smallest integer $\ell$ such that every zero-sum free sequence $T$ over $G$ of length at least $\ell$ has the following property: all nonzero elements of $G$ that do not occur as a subsequence sum of $T$ lie in a proper coset of some subgroup of $G$. We study the invariant $ν(G)$, which was introduced in Zero-Sum Theory in the 1960s.
