### Abstract

A family of sets F (and the corresponding family of 0-1 vectors) is called t-cancellative if, for all distinct t + 2 members A _{1},⋯, A _{t} and B, C ∈ F, A _{1}∪⋯∪ A _{t}∪ B ≠ A _{1}∪ ⋯ ∪ A _{t} ∪ C. Let ct(n) be the size of the largest t-cancellative family on n elements, and let ct(n, r) denote the largest r-uniform family. We improve the previous upper bounds, e.g., we show c _{2}(n) ≤ 2 ^{0.322n} (for n > n _{0}). Using an algebraic construction we show that c _{2}(n, 2k) = Θ(n ^{k}) for each k when n %rarr; ∞.

Original language | English |
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Pages (from-to) | 159-177 |

Number of pages | 19 |

Journal | Combinatorics Probability and Computing |

Volume | 21 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - Jan 2012 |

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### ASJC Scopus subject areas

- Applied Mathematics
- Theoretical Computer Science
- Computational Theory and Mathematics
- Statistics and Probability

### Cite this

**2-cancellative hypergraphs and codes.** / Füredi, Z.

Research output: Contribution to journal › Article

*Combinatorics Probability and Computing*, vol. 21, no. 1-2, pp. 159-177. https://doi.org/10.1017/S0963548311000563

}

TY - JOUR

T1 - 2-cancellative hypergraphs and codes

AU - Füredi, Z.

PY - 2012/1

Y1 - 2012/1

N2 - A family of sets F (and the corresponding family of 0-1 vectors) is called t-cancellative if, for all distinct t + 2 members A 1,⋯, A t and B, C ∈ F, A 1∪⋯∪ A t∪ B ≠ A 1∪ ⋯ ∪ A t ∪ C. Let ct(n) be the size of the largest t-cancellative family on n elements, and let ct(n, r) denote the largest r-uniform family. We improve the previous upper bounds, e.g., we show c 2(n) ≤ 2 0.322n (for n > n 0). Using an algebraic construction we show that c 2(n, 2k) = Θ(n k) for each k when n %rarr; ∞.

AB - A family of sets F (and the corresponding family of 0-1 vectors) is called t-cancellative if, for all distinct t + 2 members A 1,⋯, A t and B, C ∈ F, A 1∪⋯∪ A t∪ B ≠ A 1∪ ⋯ ∪ A t ∪ C. Let ct(n) be the size of the largest t-cancellative family on n elements, and let ct(n, r) denote the largest r-uniform family. We improve the previous upper bounds, e.g., we show c 2(n) ≤ 2 0.322n (for n > n 0). Using an algebraic construction we show that c 2(n, 2k) = Θ(n k) for each k when n %rarr; ∞.

UR - http://www.scopus.com/inward/record.url?scp=84859354545&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84859354545&partnerID=8YFLogxK

U2 - 10.1017/S0963548311000563

DO - 10.1017/S0963548311000563

M3 - Article

AN - SCOPUS:84859354545

VL - 21

SP - 159

EP - 177

JO - Combinatorics Probability and Computing

JF - Combinatorics Probability and Computing

SN - 0963-5483

IS - 1-2

ER -