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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| Date: | 2018 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Lugansk National Taras Shevchenko University
2018
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/743 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543040113475585 |
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| author | Godinho, Hemar Lemos, Abílio Marques, Diego |
| author_facet | Godinho, Hemar Lemos, Abílio Marques, Diego |
| author_sort | Godinho, Hemar |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-04-28T03:04:31Z |
| 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 \(41\leq s_A(C_{3}^{5})\leq45\). |
| first_indexed | 2025-12-02T15:40:52Z |
| format | Article |
| id | admjournalluguniveduua-article-743 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:40:52Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-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 |
| spellingShingle | Weighted zero-sum abelian groups 20D60 20K01 Godinho, Hemar Lemos, Abílio Marques, Diego Weighted zero-sum problems over \(C_3^r\) |
| title | 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_short | Weighted zero-sum problems over \(C_3^r\) |
| title_sort | weighted zero-sum problems over \(c_3^r\) |
| topic | Weighted zero-sum abelian groups 20D60 20K01 |
| topic_facet | Weighted zero-sum abelian groups 20D60 20K01 |
| 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 |