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A recursive construction of t ‐wise uniform permutations
Author(s) -
Finucane Hilary,
Peled Ron,
Yaari Yariv
Publication year - 2015
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/rsa.20509
Subject(s) - set (abstract data type) , struct , combinatorics , permutation (music) , mathematics , discrete mathematics , computer science , physics , acoustics , programming language
We present a recursive construction of a (2 t + 1)‐wise uniform set of permutations on 2 n objects using a ( 2 t + 1 ) − ( 2 n , n , · ) combinatorial design, a t ‐wise uniform set of permutations on n objects and a (2 t + 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 2 n , the first non‐trivial construction of an infinite family of t ‐wise uniform sets for t ≥ 4 . If a non‐trivial design with suitable parameters is found, it will imply a corresponding improvement in the construction. © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 46, 531–540, 2015