Sum-free sets in vector spaces over \(GF(2)\)
type: Item
instance of: scholarly article
title: Sum-free sets in vector spaces over \(GF(2)\)
zbMATH Open document ID: 0762.05018
DOI: 10.1016/0097-3165(92)90019-Q
author: W. Edwin Clark
author: John Pedersen
published in: Journal of Combinatorial Theory. Series A
publication date: 1993-01-17T00:00:00Z
review text: Let \(V(n)\) denote the standard \(n\)-dimensional vector space of \(n\)-tuples over the field \(GF(2)\). A subset \(S\) of \(V(n)\) is sum-free if \((S+S)\cap S=\emptyset\); for example, the set of all vectors with an odd number of components equal to 1 is a sum-free subset of largest size, namely \(2^{n-1}\). The authors show that any sum-free subset of size less than \(2^{n-1}\) has size at most \(5\times 2^{n-4}\) and find bounds for the size of the smallest maximal sum-free subsets. By constructing various classes of sum-free subsets they are able to give a complete list of the maximal sum-free subsets of \(V(n)\) for \(n\leq 6\) and partial information for \(n>6\).
reviewed by: John D. Dixon
Mathematics Subject Classification ID: 05B10
zbMATH DE Number: 96574
zbMATH Keywords: vector spaces over \(GF(2)\)
zbMATH Keywords: sum-free sets
MaRDI profile type: Publication
cites work: Blocking sets and partial spreads in finite projective spaces
cites work: Binary set functions and parity check matrices
cites work: Blocking sets in finite projective spaces and uneven binary codes
cites work: Q3851217
cites work: Q3694152
cites work: Some results on Ramsey numbers using sumfree sets
cites work: Q4146667
cites work: Q4068732
cites work: Maximal Sum-Free Sets of Group Elements
full work available at URL: 0097-3165(92)90019-q
OpenAlex ID: W1995661366
description: scientific article; zbMATH DE number 96574