## Abstract

The seminal complete intersection theorem of Ahlswede and Khachatrian gives the maximum cardinality of a k-uniform t-intersecting family on n points, and describes all optimal families. In recent work, we extended this theorem to the weighted setting, giving the maximum μ_{p} measure of a t-intersecting family on n points. In this work, we prove two new complete intersection theorems. The first gives the supremum μ_{p} measure of a t-intersecting family on infinitely many points, and the second gives the maximum cardinality of a subset of Z_{m} ^{n} in which any two elements x,y have t positions i_{1},…,i_{t} such that x_{ij }−y_{ij }∈{−(s−1),…,s−1}. In both cases, we determine the extremal families, whenever possible.

Original language | English |
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Pages (from-to) | 128-142 |

Number of pages | 15 |

Journal | Discrete Mathematics |

Volume | 342 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2019 |

## Keywords

- Erdos–Ko–Rado theory
- Extremal combinatorics
- Intersecting families

## All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics