Symmetric Groups and Expander Graphs
Abstract
We construct explicit generating sets S_n and \tilde S_n of the for the alternating and the symmetric groups, which turn the Cayley graphs C(Alt(n), S_n) and C(Sym(n), \tilde S_n) into a family of bounded degree expanders for all n. This answers affirmatively an old question which has been asked many times in the literature. These expanders have many applications in the theory of random walks on groups, card shuffling and other areas.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 May 2005
 arXiv:
 arXiv:math/0505624
 Bibcode:
 2005math......5624K
 Keywords:

 Group Theory;
 Combinatorics;
 Primary 20B30;
 Secondary 05C25;
 05E15;
 20C30;
 20F69
 EPrint:
 30 pages