Permutations fixing a k-set

Sean Eberhard, Kevin Ford, Ben Green

Research output: Contribution to journalArticlepeer-review


Let i(n, k) be the proportion of permutations π ∈ Sn having an invariant set of size k. In this note, we adapt arguments of the second author to prove that i(n, k) k-δ(1 + log k) -3/2 uniformly for 1 ≤ k≤ n/2, where δ =1 - 1+log log 2/log 2 . As an application, we show that the proportion of π ∈ Sn contained in a transitive subgroup not containing An is at least n-δ+o(1) if nis even.

Original languageEnglish (US)
Pages (from-to)6713-6731
Number of pages19
JournalInternational Mathematics Research Notices
Issue number21
StatePublished - 2016

ASJC Scopus subject areas

  • General Mathematics


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