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arXiv · 0905.4248

Remarks on a generalization of the Davenport constant

Michael Freeze·Wolfgang A. Schmid
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Abstract

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).

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Michael Freeze, Wolfgang A. Schmid. 2009-05-26. Remarks on a generalization of the Davenport constant. https://arxiv.org/abs/0905.4248

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