The action of a few permutations on r-tuples is quickly transitive

Joel Friedman, Antoine Joux, Yuval Roichman, Jacques Stern, Jean Pierre Tillich

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

We prove that for every r and d ≥ 2 there is a C such that for most choices of d permutations π1, π2, . . . , πd of Sn, the following holds: for any two r-tuples of distinct elements in {1, . . . , n}, there is a product of less than C log n of the πis which map the first r-tuple to the second. Although we came across this problem while studying a rather unrelated cryptographic problem, it belongs to a general context of which random Cayley graph quotients of Sn are good expanders.

Original languageEnglish
Pages (from-to)335-350
Number of pages16
JournalRandom Structures and Algorithms
Volume12
Issue number4
DOIs
StatePublished - Jul 1998
Externally publishedYes

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