Bounds on the diameter of Cayley graphs of the symmetric group
Journal of Algebraic Combinatorics, Tome 40 (2014) no. 1, pp. 1-22.

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In this paper we are concerned with the conjecture that, for any set of generators $S$ of the symmetric group $\mathrm{Sym}(n)$, the word length in terms of $S$ of every permutation is bounded above by a polynomial of $n$. We prove this conjecture for sets of generators containing a permutation fixing at least 37% of the points.
Classification : 05C25, 20B30
Mots-clés : Cayley graph, diameter, Babai's conjecture, Babai-Seress conjecture
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     author = {Bamberg, John and Gill, Nick and Hayes, Thomas P. and Helfgott, Harald A. and Seress, \'Akos and Spiga, Pablo},
     title = {Bounds on the diameter of {Cayley} graphs of the symmetric group},
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Bamberg, John; Gill, Nick; Hayes, Thomas P.; Helfgott, Harald A.; Seress, Ákos; Spiga, Pablo. Bounds on the diameter of Cayley graphs of the symmetric group. Journal of Algebraic Combinatorics, Tome 40 (2014) no. 1, pp. 1-22. https://geodesic-test.mathdoc.fr/item/JAC_2014__40_1_a12/