The base size of the symmetric group acting on subsets

Coen del Valle*, Colva Roney-Dougal

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 > 2r. The symmetric and alternating groups Sn and An admit natural primitive actions on the set of 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 Sn and An.
Original languageEnglish
Number of pages8
JournalAlgebraic Combinatorics
Publication statusAccepted/In press - 20 Mar 2024


  • Symmetric group
  • Base size
  • Hypergraph


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