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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.11312 |
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| _version_ | 1866913318667550720 |
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| author | Lemos, A. Moura, A. O. Ribas, S. Silva, A. T. |
| author_facet | Lemos, A. Moura, A. O. Ribas, S. Silva, A. T. |
| contents | Let $G$ be a group and $A\subseteq [1,\exp(G)-1]$. We define the constant ${\sf C}_A(G),$ which is the least positive integer $\ell$ such that every sequence over $G$ of length at least $\ell$ has an $A$-weighted consecutive product-one subsequence. In this paper, among other things, we prove that ${\sf C}_A(C_n^2)=4$ with $A=[1,n-1],$ and ${\sf C}(H\times K)=|H||K|$, where $H$ is a finite abelian group and $K$ is a metacyclic group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_11312 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on weighted consecutive Davenport constant Lemos, A. Moura, A. O. Ribas, S. Silva, A. T. Number Theory Let $G$ be a group and $A\subseteq [1,\exp(G)-1]$. We define the constant ${\sf C}_A(G),$ which is the least positive integer $\ell$ such that every sequence over $G$ of length at least $\ell$ has an $A$-weighted consecutive product-one subsequence. In this paper, among other things, we prove that ${\sf C}_A(C_n^2)=4$ with $A=[1,n-1],$ and ${\sf C}(H\times K)=|H||K|$, where $H$ is a finite abelian group and $K$ is a metacyclic group. |
| title | A note on weighted consecutive Davenport constant |
| topic | Number Theory |
| url | https://arxiv.org/abs/2404.11312 |