Symmetric groups and expanders

Abstract

We construct explicit generating sets Fn and Fn of the alternating and the symmetric groups, which turn the Cayley graphs C(Alt(n), Fn) and C(Sym(n), Fn) into a family of bounded degree expanders for all sufficiently large n. These expanders have many applications in the theory of random walks on groups and in other areas of mathematics. © 2005 American Mathematical Society.