Restricted inverse zero-sum problems in groups of rank 2.
type: Item
instance of: scholarly article
zbMATH Open document ID: 1252.20026
published in: The Quarterly Journal of Mathematics
publication date: 2012-06-12T00:00:00Z
full work available at URL: https://arxiv.org/abs/1007.0257
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 11P70
Mathematics Subject Classification ID: 20K01
Mathematics Subject Classification ID: 11B75
zbMATH DE Number: 6045454
zbMATH Keywords: combinatorial constants for finite Abelian groups
zbMATH Keywords: Abelian groups of rank two
zbMATH Keywords: zero-sum sequences
zbMATH Keywords: inverse zero-sum problems
author: Wolfgang A. Schmid
MaRDI profile type: Publication
OpenAlex ID: W2132115199
arXiv ID: 1007.0257
DOI: 10.1093/QMATH/HAQ042
title: Restricted inverse zero-sum problems in groups of rank 2.
review text: Let \(G\) be a finite Abelian group of exponent \(N\), and denote by \(s(G)\) the smallest integer \(k\) such that each sequence of \(\geq k\) elements of \(G\) has a subsequence of length equal to \(N\) with vanishing sum. Replacing here equality by \(\leq N\) one obtains another constant, denoted by \(\eta(G)\). The author considers groups of rank \(2\). He presents a construction of sequences of lengths \(s(G)-1\) and \(\eta(G)-1\), respectively, which do not have such subsequences, and shows that in certain cases his construction gives all such sequences. This applies in particular to groups of the form \(C_m\oplus C_m\) in the first case, and to groups of that form with \(m=2^a3^b5^c7^d\) in the second case.
reviewed by: Władysław Narkiewicz
description: scientific article; zbMATH DE number 6045454