Geodesic
Weighted zero-sum problems over $C_3^r$
Algebra and discrete mathematics, Tome 15 (2013) no. 2, pp. 201-212

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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. 
@article{ADM_2013_15_2_a5,
     author = {H. Godinho and A. Lemos and D. Marques},
     title = {Weighted zero-sum problems over $C_3^r$},
     journal = {Algebra and discrete mathematics},
     pages = {201--212},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2013_15_2_a5/}
}
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H. Godinho; A. Lemos; D. Marques. Weighted zero-sum problems over $C_3^r$. Algebra and discrete mathematics, Tome 15 (2013) no. 2, pp. 201-212. http://geodesic.mathdoc.fr/item/ADM_2013_15_2_a5/