Covering a finite abelian group by subset sums
type: Item
instance of: scholarly article
title: Covering a finite abelian group by subset sums
zbMATH Open document ID: 1049.11022
author: Yahya Ould Hamidoune
author: Oriol Serra
author: Weidong Gao
author: Anna Lladó
published in: Combinatorica
publication date: 2004-10-19T00:00:00Z
review text: Let \(G\) be an finite additive abelian group of order \(n\geq 3\), and let \(S\) be a subset of non-zero elements of \(G\). Then \(\sum(S)=\{\sum_{x\in A} x\mid A\subseteq S,\;A\neq \emptyset\}\) is the set of all subset sums of \(S\). The critical number \(c(G)\) of \(G\) is the smallest \(s\) such that the subset sums of \(\sum(S)\) cover all \(G\) for each subset \(S\subset G\{0\} \) of cardinality \(| S| \geq s\). Some years ago it has been proved that, if \(p\) is the smallest prime dividing \(n\) and \(n/p=h\) is composite, then \(c(G)=h+p-2\). In this paper the sets with \(| S| =h+p-3\) and \(\sum(S)=G\) are characterized, where \(p\geq 3\) is the smallest prime dividing \(n\), \(n/p=h\) is composite and \(n\geq 7p^2+3p\). There are also some further results for groups with odd order.
Mathematics Subject Classification ID: 11B75
Mathematics Subject Classification ID: 20K01
zbMATH DE Number: 2108656
zbMATH Keywords: subset sums
reviewed by: Joachim Piehler
MaRDI profile type: Publication
full work available at URL: s00493-003-0036-x
OpenAlex ID: W1975311321
DOI: 10.1007/S00493-003-0036-X
description: scientific article; zbMATH DE number 2108656