Modification of Griffiths' result for even integers
type: Item
instance of: scholarly article
title: Modification of Griffiths' result for even integers
zbMATH Open document ID: 1431.11040
author: Eshita Mazumdar
author: Sneh Bala Sinha
published in: The Electronic Journal of Combinatorics
publication date: 2016-12-06T00:00:00Z
full work available at URL: v23i4p18
review text: Summary: For a finite abelian group \(G\) with \(\exp(G)=n\), the arithmetical invariant \(\mathsf s_A(G)\) is defined to be the least integer \(k\) such that any sequence \(S\) with length \(k\) of elements in \(G\) has a \(A\) weighted zero-sum subsequence of length \(n\). When \(A=\{1\}\), it is \textit{the Erdős-Ginzburg-Ziv constant} and is denoted by \(\mathsf s(G)\). For certain class of sets \(A\), we already have some general bounds for these weighted constants corresponding to the cyclic group \(\mathbb{Z}_n\), which was given by Griffiths. For odd integer \(n\), Adhikari and Mazumdar generalized the above mentioned results in the sense that they hold for more sets \(A\). In the present paper we modify Griffiths' method for even \(n\) and obtain general bound for the weighted constants for certain class of weighted sets which include sets that were not covered by Griffiths for \(n\equiv 0\pmod 4\).
Mathematics Subject Classification ID: 11B75
Mathematics Subject Classification ID: 20K01
zbMATH DE Number: 6661370
zbMATH Keywords: zero-sum problems
zbMATH Keywords: Kneser's theorem
MaRDI profile type: Publication
cites work: Some zero-sum constants with weights
cites work: Davenport constant with weights and some related questions. II.
cites work: Contributions to zero-sum problems
cites work: Q3629009
cites work: On weighted zero-sum sequences
cites work: Q5495440
cites work: Generalizations of some zero sum theorems
cites work: Zero-sum problems in finite Abelian groups: a survey
cites work: Q5200682
cites work: The Erdős-Ginzberg-Ziv theorem with units
cites work: Structural additive theory. Based on courses given at Karl-Franzens-Universität Graz, Austria, 2008--2012
cites work: Abschätzung der asymptotischen Dichte von Summenmengen
cites work: A generalization of a classical zero-sum problem
cites work: Q4895030
description: scientific article; zbMATH DE number 6661370