Large convex cones in hypercubes

Zoltán Füredi, Miklós Ruszinkó

Research output: Contribution to journalArticle


A family of subsets of [n] is positive linear combination free if the characteristic vector of neither member is the positive linear combination of the characteristic vectors of some other ones. We construct a positive linear combination free family which contains (1 - o (1)) 2n subsets of [n] and we give tight bounds on the o (1) 2n term. The problem was posed by Ahlswede and Khachatrian [Cone dependence-a basic combinatorial concept, Preprint 00-117, Diskrete Strukturen in der Mathematik SFB 343, Universität Bielefeld, 2000] and the result has geometric consequences.

Original languageEnglish
Pages (from-to)1536-1541
Number of pages6
JournalDiscrete Applied Mathematics
Issue number9
Publication statusPublished - May 1 2008



  • Convex cone
  • Hypercube

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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