On base sizes for symmetric groups

@article{Burness2011OnBS,
  title={On base sizes for symmetric groups},
  author={Timothy C. Burness and R. Guralnick and J. Saxl},
  journal={Bulletin of The London Mathematical Society},
  year={2011},
  volume={43},
  pages={386-391}
}
A base of a permutation group G on a set is a subset B of such that the pointwise stabilizer of B in G is trivial. The base size of G, denoted by b(G), is the minimal cardinality of a base. Let G = Sn or An acting primitively on a set with point stabilizer H. In this note we prove that if H acts primitively on {1, . . . , n}, and does not contain An, then b(G) = 2 for all n 13. Combined with a theorem of James, this completes the classification of primitive actions of alternating and symmetric… Expand

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