## Abstract

A set of permutations L on a finite linearly ordered set Ω is said to be k-min-wise independent, k-MWI for short, if Pr (min (π(X)) = π(x)) = 1/|X| for every X ⊆ Ω such that |X| ≤ k and for every x ∈ X. (Here π(x) and π(X) denote the image of the element x or subset X of Ω under the permutation π, and Pr refers to a probability distribution on L, which we take to be the uniform distribution.) We are concerned with sets of permutations which are k-MWI families for any linear order. Indeed, we characterize such families in a way that does not involve the underlying order. As an application of this result, and using the Classification of Finite Simple Groups, we deduce a complete classification of the k-MWI families that are groups, for k ≥3.

Original language | English |
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Pages (from-to) | 3026-3033 |

Number of pages | 8 |

Journal | Communications in Algebra |

Volume | 35 |

Issue number | 10 |

DOIs | |

Publication status | Published - 1 Oct 2007 |

## Keywords

- Linear order
- Min-wise independent family
- Permutation group