Abstract
We study the natural action of Sn on the set of k-subsets of the set {1,…,n} when 1≤k≤n2. 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.
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