Abstract
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 language | English |
|---|---|
| Pages (from-to) | 6713-6731 |
| Number of pages | 19 |
| Journal | International Mathematics Research Notices |
| Volume | 2016 |
| Issue number | 21 |
| DOIs | |
| Publication status | Published - 23 Dec 2015 |
| Externally published | Yes |
Bibliographical note
Funding Information:B.G. is supported by ERC Starting grant number 279438, Approximate algebraic structure and applications, and a Simons Investigator Award. K.F. is supported by National Science Foundation grants DMS-1201442 and DMS-1501982.
Publisher Copyright:
© 2015 The Author(s) 2015. Published by Oxford University Press.
ASJC Scopus subject areas
- General Mathematics