Forbidden (0, 1)-vectors in hyperplanes of \(\mathbb{R}^n\): The restricted case
type: Item
instance of: scholarly article
title: Forbidden (0, 1)-vectors in hyperplanes of \(\mathbb{R}^n\): The restricted case
zbMATH Open document ID: 1019.05059
DOI: 10.1023/A:1024131820350
published in: Designs, Codes and Cryptography
publication date: 2003-08-21T00:00:00Z
review text: Denote \(E(n,k)\) the set of all \((0,1)\)-vectors in \(\mathbb{R}^n\) with exactly \(k\) ones. This paper tries to determine the maximum cardinality \(F(n,m,w)\) of \(X \subset E(n,m)\) such that the span \(\langle X\rangle\) does not contain any \((0,1)\)-vector with exactly \(w\) ones. The proofs use classical extremal set theoretical results, lengthy case analysis and calculations.
Mathematics Subject Classification ID: 05D05
Mathematics Subject Classification ID: 05B30
Mathematics Subject Classification ID: 05A30
Mathematics Subject Classification ID: 52C99
zbMATH DE Number: 1968853
zbMATH Keywords: combinatorial extremal theory
zbMATH Keywords: \((0, 1)\)-vectors
zbMATH Keywords: dimension constraint
zbMATH Keywords: forbidden weights
zbMATH Keywords: nontrivial intersecting systems
author: Harout Aydinian
author: Levon H. Khachatrian
author: Rudolf Ahlswede
reviewed by: Péter L. Erdős
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1968853