Symmetric Groups and Expander Graphs
Group Theory
2007-05-23 v1 Combinatorics
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.
Cite
@article{arxiv.math/0505624,
title = {Symmetric Groups and Expander Graphs},
author = {Martin Kassabov},
journal= {arXiv preprint arXiv:math/0505624},
year = {2007}
}
Comments
30 pages