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arXiv · 1802.01977

Roots of Polynomials and The Derangement Problem

Lior Bary-Soroker·Ofir Gorodetsky
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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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Lior Bary-Soroker, Ofir Gorodetsky. 2018-02-06. Roots of Polynomials and The Derangement Problem. https://doi.org/10.1080/00029890.2018.1521231

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