Geometric representation of 3-restricted min-wise independent sets of permutations

TL;DR

This paper explores the structure of 3-restricted min-wise independent permutation sets and shows their isomorphism to specific subsets of hypercube vertices with fixed pairwise distances.

Contribution

It establishes a novel geometric characterization of 3-restricted min-wise independent permutation sets through hypercube subset isomorphism.

Findings

Proves the isomorphism between permutation sets and hypercube vertex subsets.

Characterizes the properties of 3-restricted min-wise independent sets.

Provides a geometric perspective on permutation set structure.

Abstract

We study properties of 3-restricted min-wise independent sets of permutations and prove that the class of these sets is isomorphic to the class of subsets of vertices of multi-dimentional hypercube of certain size with certain pair-wise distances fixed.