Maximum number of constant weight vertices of the unit \(n\)-cube contained in a \(k\)-dimensional subspace
type: Item
instance of: scholarly article
title: Maximum number of constant weight vertices of the unit \(n\)-cube contained in a \(k\)-dimensional subspace
zbMATH Open document ID: 1046.05076
author: Levon H. Khachatrian
author: Harout Aydinian
author: Rudolf Ahlswede
published in: Combinatorica
publication date: 2004-09-07T00:00:00Z
review text: The largest intersection \(| U\cap E(n,w)| \) is determined where \(U\) is a \(k\)-dimensional subspace of \(\mathbb{R}^n\) and \(E(n,w)\) is the set of length-\(n\) 0-1 sequences with \(w\) 1-entries. It is \(k \choose w\) for \(w\leq k/2\), \({{2(k-w)} \choose {k-w}}2^{2w-k}\) for \(k/2<w<k-1\), and \(2^{k-1}\) for \(k-1\leq w \leq n/2\). An extension of Erdős-Moser type and one on multisets are also given.
Mathematics Subject Classification ID: 05D05
Mathematics Subject Classification ID: 15A03
zbMATH DE Number: 2099001
zbMATH Keywords: extremal set theory
reviewed by: Péter Komjáth
MaRDI profile type: Publication
full work available at URL: s00493-003-0011-6
OpenAlex ID: W2072189964
DOI: 10.1007/S00493-003-0011-6
description: scientific article; zbMATH DE number 2099001