Bounds on the diameter of Cayley graphs of the symmetric group

ISSN
0925-9899
Date Issued
2013
Author(s)
Bamberg, John
Gill, Nick
Hayes, Thomas P.
Seress, Ákos
Spiga, Pablo
DOI
10.1007/s10801-013-0476-3
Abstract
In this paper we are concerned with the conjecture that, for any set of generators S of the symmetric group 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.
Subjects