关于Davenport常数推广的注记
Remarks on a generalization of the Davenport constant
摘要：
本文研究了达文波特常数的推广。对于有限阿贝尔群$G$和正整数$k$，令$D_k(G)$表示最小的$\ell$，使得$G$上长度至少为$\ell$的每个序列具有$k$不相交的非空零和序列。对于一般的$G$，在已有结果的基础上，研究了这些不变量的上、下界，证明了序列$(D_k(G))_{k\in\mathbb{N}}$最终是一个带差等差数列$\exp(G)$，并讨论了由此引起的几个问题.对于初等2-群，详细研究了$D_k(G)$;特别是，确定了秩为4和5的群的精确值（对于秩至多为3的群，它们是已知的）。
英文摘要：
A generalization of the Davenport constant is investigated. For a finite abelian group $G$ and a positive integer $k$, let $D_k(G)$ denote the smallest $\ell$ such that each sequence over $G$ of length at least $\ell$ has $k$ disjoint non-empty zero-sum subsequences. For general $G$, expanding on known results, upper and lower bounds on these invariants are investigated and it is proved that the sequence $(D_k(G))_{k\in\mathbb{N}}$ is eventually an arithmetic progression with difference $\exp(G)$, and several questions arising from this fact are investigated. For elementary 2-groups, $D_k(G)$ is investigated in detail; in particular, the exact values are determined for groups of rank four and five (for rank at most three they were already known).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
