Statistics for Sn acting on k-sets

Gill, N. and Lodà, B. (2022). Statistics for Sn acting on k-sets. Journal of Algebra, 607(Part A) pp. 286–299.



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.

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