A recursive construction of t-wise uniform permutations
Combinatorics
2017-03-14 v2 Probability
Abstract
We present a recursive construction of a (2t + 1)-wise uniform set of permutations on 2n objects using a (2t + 1) - (2n, n, \cdot) combinatorial design, a t-wise uniform set of permutations on n objects and a (2t+1)-wise uniform set of permutations on n objects. Using the complete design in this procedure gives a t-wise uniform set of permutations on n objects whose size is at most t^2n, the first non-trivial construction of an infinite family of t-wise uniform sets for t \geq 4. If a non-trivial design with suitable parameters is found, it will imply a corresponding improvement in the construction.
Cite
@article{arxiv.1201.4960,
title = {A recursive construction of t-wise uniform permutations},
author = {Hilary Finucane and Ron Peled and Yariv Yaari},
journal= {arXiv preprint arXiv:1201.4960},
year = {2017}
}