%0 Journal Article
%T Bounds on the diameter of Cayley graphs of the symmetric group
%A John Bamberg
%A Nick Gill
%A Thomas Hayes
%A Harald Helfgott
%A ¨¢kos Seress
%A Pablo Spiga
%J Mathematics
%D 2012
%I arXiv
%X In this paper we are concerned with the conjecture that, for any set of generators S of the symmetric group of degree 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.
%U http://arxiv.org/abs/1205.1596v1