Symmetric Groups and Expander Graphs

Details Symmetric Groups and Expander Graphs Symmetric Groups and Expander Graphs

2005-05-28

arxiv.org/abs/math/0505624v1

Mathematics

Group Theory

30 pages

Scientific paper

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.

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