Roots of Polynomials and the Derangement Problem

Lior Bary-Soroker; Ofir Gorodetsky

doi:10.1080/00029890.2018.1521231

Roots of Polynomials and the Derangement Problem

Lior Bary-Soroker, Ofir Gorodetsky

Tel Aviv University

Research output: Contribution to journal › Comment/debate

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.

Original language	English
Pages (from-to)	934-938
Number of pages	5
Journal	American Mathematical Monthly
Volume	125
Issue number	10
DOIs	https://doi.org/10.1080/00029890.2018.1521231
State	Published - 26 Nov 2018

Keywords

11T55
MSC: Primary 60C05
Secondary 11T06

All Science Journal Classification (ASJC) codes

General Mathematics

Access to Document

10.1080/00029890.2018.1521231

Cite this

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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.",

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KW - Secondary 11T06

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M3 - تعليقَ / نقاش

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JF - American Mathematical Monthly

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ER -

Roots of Polynomials and the Derangement Problem

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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