On the Diameter of Random Cayley Graphs of the Symmetric Group
1992 ◽
Vol 1
(3)
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pp. 201-208
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Let σ, π be two permutations selected at random from the uniform distribution on the symmetric group Sn. By a result of Dixon [5], the subgroup G generated by σ, π is almost always (i.e. with probability approaching 1 as n → ∞) either Sn or the alternating group An. We prove that the diameter of the Cayley graph of G defined by {σ, π} is almost always not greater than exp ((½ + o(l)). (In n)2).
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2016 ◽
Vol 93
(3)
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pp. 441-446
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2019 ◽
Vol 18
(12)
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pp. 1950237
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