The extent to which subsets are additively closed
type: Item
instance of: scholarly article
title: The extent to which subsets are additively closed
zbMATH Open document ID: 1208.11034
author: Sophie Huczynska
author: Gary L. Mullen
author: Joseph L. Yucas
published in: Journal of Combinatorial Theory. Series A
publication date: 2009-06-17T00:00:00Z
review text: In subset sum theory, sum-free sets have been the subject of many studies. In this paper, the authors consider the \(r\)-closed set, and in this case, the sum-free set is \(0\)-closed. An \(r\)-closed set is a comprehensive generalization of a sum-free set. There are many problems that can be considered on an \(r\)-closed set according to two different points of view, direct problem and inverse problem. In this paper, the authors investigate direct problems. They obtain some results on the combinatorial constant \(r(S)\), and in particular, the result obtained in cyclic groups of prime order can be considered as a generalization of the Cauchy-Davenport theorem.
reviewed by: Jujuan Zhuang
Mathematics Subject Classification ID: 11B75
Mathematics Subject Classification ID: 20K01
Mathematics Subject Classification ID: 11B13
zbMATH DE Number: 5565589
zbMATH Keywords: finite field
zbMATH Keywords: integers modulo \(p\)
zbMATH Keywords: sum-free set
zbMATH Keywords: Cauchy-Davenport theorem
MaRDI profile type: Publication
full work available at URL: j.jcta.2008.11.007
OpenAlex ID: W2157821161
cites work: Q3470561
cites work: On the number of monochromatic Schur triples.
cites work: A Historical Note
cites work: THE CAMERON–ERDOS CONJECTURE
cites work: Cameron-Erdős modulo a prime
cites work: A Generalisation of the Theorem of Cauchy and Davenport
cites work: Maximal sum-free sets in finite abelian groups
cites work: Some Ramsey and anti–Ramsey results in finite groups
cites work: Q3799811
cites work: Q5393666
cites work: The Critical Pairs of Subsets of a Group of Prime Order
cites work: Maximal Sum-Free Sets of Group Elements
DOI: 10.1016/J.JCTA.2008.11.007
description: scientific article; zbMATH DE number 5565589