Statistics for S acting on k-sets

Nick Gill, Bianca Lodà

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Article numberS0021869321005366
JournalJournal of Algebra
Issue number00
Early online date15 Nov 2021
Publication statusE-pub ahead of print - 15 Nov 2021


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


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