Subset sums in binary spaces
type: Item
instance of: scholarly article
title: Subset sums in binary spaces
zbMATH Open document ID: 0772.11004
DOI: 10.1016/0195-6698(92)90028-X
author: Gilles Zémor
published in: European Journal of Combinatorics
publication date: 1992-09-27T00:00:00Z
review text: Sei \(G=Z_ 2^ L\) die Gruppe der binären Vektoren der Länge \(L\). Dann zeigt Verf. den folgenden Satz (Theorem 1.4): Sei \(S\) eine Teilmenge von \(G\) und \(k\in\mathbb{N}_ 0\). Dann gilt entweder (i) es gibt eine echte Untergruppe \(H\) von \(G\), so daß \(| S+H|-| S|<| H|+k\) oder (ii) für jede Teilmenge \(T\) von \(G\) mit \(k\leq| T|^ 2-2\) und \(2\leq| G|-| S+T|\) gilt \(| S+T|\geq | S|+| T|+k\). Am Schluß wird auf zwei Anwendungen hingewiesen.
Mathematics Subject Classification ID: 11B05
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 20K01
zbMATH DE Number: 64848
zbMATH Keywords: sum sets
zbMATH Keywords: lower bound
zbMATH Keywords: cardinality
zbMATH Keywords: sets of binary vectors of given length
zbMATH Keywords: abelian group
zbMATH Keywords: Kneser's theorem
reviewed by: Erich Härtter
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 64848