TY - JOUR

T1 - The action of a few permutations on r-tuples is quickly transitive

AU - Friedman, Joel

AU - Joux, Antoine

AU - Roichman, Yuval

AU - Stern, Jacques

AU - Tillich, Jean Pierre

PY - 1998/7

Y1 - 1998/7

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0032337421&partnerID=8YFLogxK

U2 - 10.1002/(SICI)1098-2418(199807)12:4<335::AID-RSA2>3.0.CO;2-U

DO - 10.1002/(SICI)1098-2418(199807)12:4<335::AID-RSA2>3.0.CO;2-U

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AN - SCOPUS:0032337421

SN - 1042-9832

VL - 12

SP - 335

EP - 350

JO - Random Structures and Algorithms

JF - Random Structures and Algorithms

IS - 4

ER -