Min-wise independent groups with respect to any linear order
نویسندگان
چکیده
A finite permutation group G on a linearly ordered set Ω is said to be a k-min-wise independent group, k-MWI for short, if Pr(minπ(X) = π(x)) = 1/|X| for every X ⊆ Ω such that |X| ≤ k and for every x ∈ X. We are concerned with the case of k-MWI groups for any linear order. Indeed, we prove that a permutation group G is k-MWI with respect to any linear order if and only if for every h ≤ k and for every h-set X the group GX is transitive on X. Next we use this result to deduce a complete classification of these groups for k ≥ 3.
منابع مشابه
Min-wise independent families with respect to any linear order
A set of permutations S on a finite linearly ordered set Ω is said to be k-min-wise independent, k-MWI for short, if Pr(minπ(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 S , which we take to be the uniform distribution.) W...
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