Bounds on the diameter of Cayley graphs of the symmetric group

John Bamberg, Nick Gill, Thomas Hayes, Harald Helfgott, Ákos Seress, Pablo Spiga

Published 2012-05-08Version 1

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.