On the inverse problem of the $k$-th Davenport constants for groups of rank $2$

Qinghai Zhong

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arXiv · 2503.21231

On the inverse problem of the $k$-th Davenport constants for groups of rank $2$

Qinghai Zhong

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Abstract

For a finite abelian group $G$ and a positive integer $k$, let $\mathsf{D}_k(G)$ denote the smallest integer $\ell$ such that each sequence over $G$ of length at least $\ell$ has $k$ disjoint nontrivial zero-sum subsequences. It is known that $\mathsf D_k(G)=n_1+kn_2-1$ if $G\cong C_{n_1}\oplus C_{n_2}$ is a rank $2$ group, where $1<n_1\t n_2$. We investigate the associated inverse problem for rank $2$ groups, that is, characterizing the structure of zero-sum sequences of length $\mathsf D_k(G)$ that can not be partitioned into $k+1$ nontrivial zero-sum subsequences.

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Qinghai Zhong. 2025-03-27. On the inverse problem of the $k$-th Davenport constants for groups of rank $2$. https://arxiv.org/abs/2503.21231

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