$Weighted zero-sum problems over $C_3^r$$

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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Дата:	2018
Автори:	Godinho, Hemar, Lemos, Abílio, Marques, Diego
Формат:	Стаття
Мова:	English
Опубліковано:	Lugansk National Taras Shevchenko University 2018
Теми:	Weighted zero-sum abelian groups 20D60 20K01
Онлайн доступ:	https://admjournal.luguniv.edu.ua/index.php/adm/article/view/743
Теги:	Додати тег Немає тегів, Будьте першим, хто поставить тег для цього запису!
Назва журналу:	Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics

id	admjournalluguniveduua-article-743
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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
institution	Algebra and Discrete Mathematics
baseUrl_str
datestamp_date	2018-04-28T03:04:31Z
collection	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	2025-12-02T15:40:52Z
last_indexed	2025-12-02T15:40:52Z
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Weighted zero-sum problems over \(C_3^r\)

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