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Algebra and Discrete Mathematics, 2013, Volume 15, Issue 2, Pages 201–212
(Mi adm421)
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This article is cited in 2 scientific papers (total in 2 papers)
RESEARCH ARTICLE
Weighted zero-sum problems over $C_3^r$
H. Godinhoa, A. Lemosb, D. Marquesa a Departamento de Matemática, Universidade de Brasília, Brasília-DF, Brazil
b Departamento de Matemática, Universidade Federal de Viçosa, Viçosa-MG, Brazil
Abstract:
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 $41\leq s_A(C_{3}^{5})\leq45$.
Keywords:
Weighted zero-sum, abelian groups.
Received: 13.12.2011 Revised: 26.06.2012
Citation:
H. Godinho, A. Lemos, D. Marques, “Weighted zero-sum problems over $C_3^r$”, Algebra Discrete Math., 15:2 (2013), 201–212
Linking options:
https://www.mathnet.ru/eng/adm421 https://www.mathnet.ru/eng/adm/v15/i2/p201
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Abstract page: | 211 | Full-text PDF : | 61 | References: | 51 |
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