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Roots of polynomials and the derangement problem

Abstract:

We present a new killing-a-fly-with-a-sledgehammer proof of one of the oldest results in probability which says that the probability that a random permutation on n elements has no fixed points tends to e-1 as n tends to infinity. Our proof stems from the connection between permutations and polynomials over finite fields and is based on an independence argument, which is trivial in the polynomial world.

Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1080/00029890.2018.1521231

Authors


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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Publisher:
Taylor and Francis Publisher's website
Journal:
American Mathematical Monthly Journal website
Volume:
125
Issue:
10
Pages:
934-938
Publication date:
2018-12-01
Acceptance date:
2018-01-16
DOI:
EISSN:
1930-0972
ISSN:
0002-9890
Language:
English
Keywords:
Pubs id:
1145837
Local pid:
pubs:1145837
Deposit date:
2020-11-16

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