### Abstract

For n, k and t such that 1 < t < k < n, a set F of subsets of [n] has the (k, t)-threshold property if every k-subset of [n] contains at least t sets from F and every (k - 1)-subset of [n] contains less than t sets from F. The minimal number of sets in a set system with this property is denoted by m (n, k, t). In this paper we determine m (n, 4, 3) exactly for n sufficiently large, and we show that m (n, k, 2) is asymptotically equal to the generalized Turán number T_{k - 1} (n, k, 2).

Original language | English |
---|---|

Pages (from-to) | 3097-3111 |

Number of pages | 15 |

Journal | Discrete Mathematics |

Volume | 306 |

Issue number | 23 SPEC. ISS. |

DOIs | |

Publication status | Published - Dec 6 2006 |

### Keywords

- Extremal problem
- Packing
- Set system

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

## Fingerprint Dive into the research topics of 'On set systems with a threshold property'. Together they form a unique fingerprint.

## Cite this

Füredi, Z., Sloan, R. H., Takata, K., & Turán, G. (2006). On set systems with a threshold property.

*Discrete Mathematics*,*306*(23 SPEC. ISS.), 3097-3111. https://doi.org/10.1016/j.disc.2006.06.001