Journal article
Permutations fixing a k-set
- 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+logk)−3/2 uniformly for 1≤k≤n/2, where δ=1−1+loglog2log2. 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 n is even.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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- Files:
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(Accepted manuscript, pdf, 233.3KB)
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- Publisher copy:
- 10.1093/imrn/rnv371
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Authors
Bibliographic Details
- Publisher:
- Oxford University Press Publisher's website
- Journal:
- International Mathematics Research Notices Journal website
- Volume:
- 2016
- Issue:
- 21
- Pages:
- 6713-6731
- Publication date:
- 2015-12-23
- Acceptance date:
- 2015-11-04
- DOI:
- EISSN:
-
1687-0247
- ISSN:
-
1073-7928
- Source identifiers:
-
807649
Item Description
- Keywords:
- Pubs id:
-
pubs:807649
- UUID:
-
uuid:3672bcb8-66e4-4bd4-9530-0512d179ceab
- Local pid:
- pubs:807649
- Deposit date:
- 2018-07-18
Terms of use
- Copyright holder:
- Eberhard et al
- Copyright date:
- 2015
- Notes:
- © The Author(s) 2015. This is the accepted manuscript version of the article. The final version is available online from Oxford University Press at: https://doi.org/10.1093/imrn/rnv371
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