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 -