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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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Publisher copy:
10.1093/imrn/rnv371

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
Magdalen College
Role:
Author
ORCID:
0000-0002-2224-1193
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
Keywords:
Pubs id:
pubs:807649
UUID:
uuid:3672bcb8-66e4-4bd4-9530-0512d179ceab
Local pid:
pubs:807649
Deposit date:
2018-07-18

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