On the inverse problem of the $k$-th Davenport constants for groups of rank $2$
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917969008787456 |
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| author | Zhong, Qinghai |
| author_facet | Zhong, Qinghai |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_21231 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the inverse problem of the $k$-th Davenport constants for groups of rank $2$ Zhong, Qinghai Combinatorics Number Theory 11B30, 11P70 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. |
| title | On the inverse problem of the $k$-th Davenport constants for groups of rank $2$ |
| topic | Combinatorics Number Theory 11B30, 11P70 |
| url | https://arxiv.org/abs/2503.21231 |