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On the Diameter of Random Cayley Graphs of the Symmetric Group

  • L. Babai (a1) and G. L. Hetyei (a2)
Abstract

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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[1]Babai L. and Seress Á. (1988) On the Diameter of the Cayley Graphs of the Symmetric Group. J. Combinatorial Theory, Ser. A 49 175179.
[2]Babai L. (1989) The Probability of Generating the Symmetric Group. J. Combinatorial Theory. Ser. A 52 148153.
[3]Babai L., Hetyei G., Kantor W. M., Lubotsky A. and Seress Á. (1990) On the diameter of finite groups. In: Proc. 31st IEEE Symp. on Foundations of Computer Science, St. Louis MO.857865.
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Combinatorics, Probability and Computing
  • ISSN: 0963-5483
  • EISSN: 1469-2163
  • URL: /core/journals/combinatorics-probability-and-computing
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