Roots of Polynomials and the Derangement Problem

Lior Bary-Soroker, Ofir Gorodetsky

Research output: Contribution to journalComment/debate

4 Scopus citations


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 languageEnglish
Pages (from-to)934-938
Number of pages5
JournalAmerican Mathematical Monthly
Issue number10
StatePublished - 26 Nov 2018


FundersFunder number
Israel Science Foundation


    • 11T55
    • MSC: Primary 60C05
    • Secondary 11T06


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