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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| Accès en ligne: | https://arxiv.org/abs/2510.14215 |
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| _version_ | 1866915557212684288 |
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| author | Hui, Wanzhen Li, Xue |
| author_facet | Hui, Wanzhen Li, Xue |
| contents | Let $G$ be an additive finite abelian group, and let $\mathrm{disc}(G)$ denote the smallest positive integer $t$ with the property that every sequence $S$ over $G$ with length $|S|\geq t $ contains two nonempty zero-sum subsequences of distinct lengths. In recent years, Gao et al. established the exact value of $\mathrm{disc}(G)$ for all finite abelian groups of rank $2$ and resolved the corresponding inverse problem for the group $C_n \oplus C_n$. In this paper, we characterize the structure of sequences $S$ over $G = C_n \oplus C_{nm}$ (where $m\geq 2$) when $|S| = \mathrm{disc}(G)- 1$ and all nonempty zero-sum subsequences of $S$ have the same length. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_14215 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The structure of sequences with zero-sum subsequences of the same length on finite abelian groups of rank two Hui, Wanzhen Li, Xue Combinatorics Let $G$ be an additive finite abelian group, and let $\mathrm{disc}(G)$ denote the smallest positive integer $t$ with the property that every sequence $S$ over $G$ with length $|S|\geq t $ contains two nonempty zero-sum subsequences of distinct lengths. In recent years, Gao et al. established the exact value of $\mathrm{disc}(G)$ for all finite abelian groups of rank $2$ and resolved the corresponding inverse problem for the group $C_n \oplus C_n$. In this paper, we characterize the structure of sequences $S$ over $G = C_n \oplus C_{nm}$ (where $m\geq 2$) when $|S| = \mathrm{disc}(G)- 1$ and all nonempty zero-sum subsequences of $S$ have the same length. |
| title | The structure of sequences with zero-sum subsequences of the same length on finite abelian groups of rank two |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2510.14215 |