Weighted sums in finite cyclic groups
type: Item
instance of: scholarly article
title: Weighted sums in finite cyclic groups
zbMATH Open document ID: 1052.11014
author: Yanyan Li
published in: Discrete Mathematics
publication date: 2004-08-06T00:00:00Z
review text: Let \(C_n\) be the cyclic group of \(n\) elements, \(p\) be a prime, and \(k\in\mathbb{N}\). Let \(\{w_1,\dots,w_k\}\) be a sequence of \(k\) integers such that \(w_1+\cdots+ w_k \equiv 0\pmod{p^2}\). Then, for every sequence \(a_1,a_2,\dots\), of \(p^2+1\) elements in \(C_{p^2}\), there are \(k\) distinct indices \(i_1,i_2,\dots,i_k\) such that \(w_1a_{i_1}+ \cdots+ a_{i_k}=0\). This generalizes a result of \textit{Y. O. Hamidoune} [Discrete Math. 162, No. 1--3, 127--132 (1996; Zbl 0872.11016).
Mathematics Subject Classification ID: 11B75
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 20K01
zbMATH DE Number: 2083735
zbMATH Keywords: zero-sum
zbMATH Keywords: cyclic group
zbMATH Keywords: sequence
reviewed by: Erich Härtter
MaRDI profile type: Publication
full work available at URL: j.disc.2004.02.001
OpenAlex ID: W2068282874
cites work: Q4284607
cites work: A lattice point problem and additive number theory
cites work: On the Erdős-Ginzburg-Ziv theorem and the Ramsey numbers for stars and matchings
cites work: Q3137175
cites work: Zero-sum problems -- a survey
cites work: On the Addition of Residue Classes
cites work: Q5841589
cites work: On zero-sum subsequences of restricted size
cites work: Two addition theorems on groups of prime order
cites work: A combinatorial problem on finite abelian groups
cites work: An addition theorem for finite cyclic groups
cites work: Q4397553
cites work: On weighted sums in abelian groups
DOI: 10.1016/J.DISC.2004.02.001
description: scientific article; zbMATH DE number 2083735