Weighted zero-sum problems over \(C_3^r\)
Let \(C_n\) be the cyclic group of order \(n\) and set \(s_{A}(C_n^r)\) as the smallest integer \(\ell\) such that every sequence \(\mathcal{S}\) in \(C_n^r\) of length at least \(\ell\) has an \(A\)-zero-sum subsequence of length equal to \(\exp(C_n^r)\), for \(A=\{-1,1\}\). In this paper, among ot...
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Lugansk National Taras Shevchenko University
2018
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oai:ojs.admjournal.luguniv.edu.ua:article-7432018-04-28T03:04:31Z Weighted zero-sum problems over \(C_3^r\) Godinho, Hemar Lemos, Abílio Marques, Diego Weighted zero-sum, abelian groups 20D60, 20K01 Let \(C_n\) be the cyclic group of order \(n\) and set \(s_{A}(C_n^r)\) as the smallest integer \(\ell\) such that every sequence \(\mathcal{S}\) in \(C_n^r\) of length at least \(\ell\) has an \(A\)-zero-sum subsequence of length equal to \(\exp(C_n^r)\), for \(A=\{-1,1\}\). In this paper, among other things, we give estimates for \(s_A(C_3^r)\), and prove that \(s_A(C_{3}^{3})=9\), \(s_A(C_{3}^{4})=21\) and \(41\leq s_A(C_{3}^{5})\leq45\). Lugansk National Taras Shevchenko University 2018-04-26 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/743 Algebra and Discrete Mathematics; Vol 15, No 2 (2013) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/743/pdf Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
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| datestamp_date |
2018-04-28T03:04:31Z |
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OJS |
| language |
English |
| topic |
Weighted zero-sum abelian groups 20D60 20K01 |
| spellingShingle |
Weighted zero-sum abelian groups 20D60 20K01 Godinho, Hemar Lemos, Abílio Marques, Diego Weighted zero-sum problems over \(C_3^r\) |
| topic_facet |
Weighted zero-sum abelian groups 20D60 20K01 |
| format |
Article |
| author |
Godinho, Hemar Lemos, Abílio Marques, Diego |
| author_facet |
Godinho, Hemar Lemos, Abílio Marques, Diego |
| author_sort |
Godinho, Hemar |
| title |
Weighted zero-sum problems over \(C_3^r\) |
| title_short |
Weighted zero-sum problems over \(C_3^r\) |
| title_full |
Weighted zero-sum problems over \(C_3^r\) |
| title_fullStr |
Weighted zero-sum problems over \(C_3^r\) |
| title_full_unstemmed |
Weighted zero-sum problems over \(C_3^r\) |
| title_sort |
weighted zero-sum problems over \(c_3^r\) |
| description |
Let \(C_n\) be the cyclic group of order \(n\) and set \(s_{A}(C_n^r)\) as the smallest integer \(\ell\) such that every sequence \(\mathcal{S}\) in \(C_n^r\) of length at least \(\ell\) has an \(A\)-zero-sum subsequence of length equal to \(\exp(C_n^r)\), for \(A=\{-1,1\}\). In this paper, among other things, we give estimates for \(s_A(C_3^r)\), and prove that \(s_A(C_{3}^{3})=9\), \(s_A(C_{3}^{4})=21\) and \(41\leq s_A(C_{3}^{5})\leq45\). |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/743 |
| work_keys_str_mv |
AT godinhohemar weightedzerosumproblemsoverc3r AT lemosabilio weightedzerosumproblemsoverc3r AT marquesdiego weightedzerosumproblemsoverc3r |
| first_indexed |
2025-07-17T10:34:39Z |
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2025-07-17T10:34:39Z |
| _version_ |
1837889990105759744 |