## Abstract

We study the natural action of Sn on the set of k-subsets of the set {1, . . . , n} when 1 ≤k ≤ n/2. For this action we calculate the maximum size of a minimal base, the height and the maximum length of an irredundant base.

Here a base is a set with trivial pointwise stabilizer, the height is the maximum size of a subset with the property that its pointwise stabilizer is not equal to the pointwise stabilizer of any proper subset, and an irredundant base can be thought of as a chain of (pointwise) set-stabilizers for which all containments are proper.

Here a base is a set with trivial pointwise stabilizer, the height is the maximum size of a subset with the property that its pointwise stabilizer is not equal to the pointwise stabilizer of any proper subset, and an irredundant base can be thought of as a chain of (pointwise) set-stabilizers for which all containments are proper.

Original language | English |
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Article number | S0021869321005366 |

Journal | Journal of Algebra |

Volume | 00 |

Issue number | 00 |

Early online date | 15 Nov 2021 |

DOIs | |

Publication status | E-pub ahead of print - 15 Nov 2021 |

## Keywords

- permutation group
- height of a permutation group
- relational complexity
- base size