## Abstract

Let C be a conjugacy class in the alternating group A_{n}, and let supp(C) be the number of nonfixed digits under the action of a permutation in C. For every 1 > δ > 0 and n ≥5 there exists a constant c = c(δ) > 0 such that if supp(C) ≥ δn then the undirected Cayley graph X(A_{n}, C) is a c expander. A family of such Cayley graphs with supp(C) = o(√n) is not a family of c-expanders. For every δ > 0, if supp(C) ≥ √3n then sets of vertices of order at most (1/2 - δ)(n - (n/supp(C)))! in X(A_{n}, C) expand. The proof of the last result combines spectral and representation theory techniques with direct combinatorial arguments.

Original language | English |
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Pages (from-to) | 281-297 |

Number of pages | 17 |

Journal | Journal of Combinatorial Theory. Series A |

Volume | 79 |

Issue number | 2 |

DOIs | |

State | Published - Aug 1997 |

Externally published | Yes |

### Bibliographical note

Funding Information:* Partially sponsored by the Wolfson fellowship and the Hebrew University.

### Funding

* Partially sponsored by the Wolfson fellowship and the Hebrew University.

Funders | Funder number |
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Hebrew University of Jerusalem |