Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 5
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Helfgott, Harald A. Seress, Ákos and Zuk, Andrzej 2015. Random generators of the symmetric group: Diameter, mixing time and spectral gap. Journal of Algebra, Vol. 421, p. 349.

    Kraft, Benjamin 2015. Diameters of Cayley graphs generated by transposition trees. Discrete Applied Mathematics, Vol. 184, p. 178.

    Schlage-Puchta, Jan-Christoph 2012. Applications of character estimates to statistical problems for the symmetric group. Combinatorica, Vol. 32, Issue. 3, p. 309.

    Gamburd, A. Hoory, S. Shahshahani, M. Shalev, A. and Virág, B. 2009. On the girth of random Cayley graphs. Random Structures and Algorithms, Vol. 35, Issue. 1, p. 100.

    Chung, F. R. K. and Yau, S.-T. 1995. Eigenvalues of Graphs and Sobolev Inequalities. Combinatorics, Probability and Computing, Vol. 4, Issue. 01, p. 11.

  • Combinatorics, Probability and Computing, Volume 1, Issue 3
  • September 1992, pp. 201-208

On the Diameter of Random Cayley Graphs of the Symmetric Group

  • L. Babai (a1) and G. L. Hetyei (a2)
  • DOI:
  • Published online: 01 September 2008

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).

Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1]L. Babai and Á. Seress (1988) On the Diameter of the Cayley Graphs of the Symmetric Group. J. Combinatorial Theory, Ser. A 49 175179.

[2]L. Babai (1989) The Probability of Generating the Symmetric Group. J. Combinatorial Theory. Ser. A 52 148153.

[4]J. D. Bovey (1980) The probability that some power of a permutation has small degree. Bull. London Math. Soc. 12 4751.

[5]J. D. Dixon (1969) The Probability of Generating the Symmetric Group. Math.Z. 110 199205.

[6]P. Erdős and P. Turán (1965) On some problems of a Statistical Group-Theory I. Wahrscheinlichkeitstheorie u. verw. Geb. 4 175186.

[7]P. Erdős and P. Turán (1967) On some problems of a Statistical Group-Theory II. Acta Math. Acad. Sci. Hung. 18 151163.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Combinatorics, Probability and Computing
  • ISSN: 0963-5483
  • EISSN: 1469-2163
  • URL: /core/journals/combinatorics-probability-and-computing
Please enter your name
Please enter a valid email address
Who would you like to send this to? *