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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| Datum: | 2018 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Lugansk National Taras Shevchenko University
2018
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| Schlagworte: | |
| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/743 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| Zusammenfassung: | 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 \(41\leq s_A(C_{3}^{5})\leq45\). |
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