## Abstract

A base for a permutation group

*G*acting on a set Ω is a subset*B*of Ω such that the pointwise stabiliser*G*(_{B}) is trivial. Let*n*and*r*be positive integers with*n*> 2*r*. The symmetric and alternating groups S_{n}and A*admit natural primitive actions on the set of*_{n}*r*-element subsets of {1,2,...,*n*}. Building on work of Halasi [8], we provide explicit expressions for the base sizes of all of these actions, and hence determine the base size of all primitive actions of S*and A*_{n}*.*_{n}Original language | English |
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Number of pages | 8 |

Journal | Algebraic Combinatorics |

Publication status | Accepted/In press - 20 Mar 2024 |

## Keywords

- Symmetric group
- Base size
- Hypergraph