### Abstract

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)) 2^{n} subsets of [n] and we give tight bounds on the o (1) 2^{n} 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 language | English |
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Pages (from-to) | 1536-1541 |

Number of pages | 6 |

Journal | Discrete Applied Mathematics |

Volume | 156 |

Issue number | 9 |

DOIs | |

Publication status | Published - máj. 1 2008 |

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics

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## Cite this

Füredi, Z., & Ruszinkó, M. (2008). Large convex cones in hypercubes.

*Discrete Applied Mathematics*,*156*(9), 1536-1541. https://doi.org/10.1016/j.dam.2006.11.018