Polynomial Factorization Statistics and Point Configurations in ℝ3

Abstract We use combinatorial methods to relate the expected values of polynomial factorization statistics over $\mathbb{F}_q$ to the cohomology of ordered configurations in $\mathbb{R}^3$ as a representation of the symmetric group. Our method gives a new proof of the twisted Grothendieck–Lefschetz...

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Bibliographic Details
Published in:International mathematics research notices 2020-12, Vol.2020 (24), p.10154-10179
Main Author: Hyde, Trevor
Format: Article
Language:English
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Summary:Abstract We use combinatorial methods to relate the expected values of polynomial factorization statistics over $\mathbb{F}_q$ to the cohomology of ordered configurations in $\mathbb{R}^3$ as a representation of the symmetric group. Our method gives a new proof of the twisted Grothendieck–Lefschetz formula for squarefree polynomial factorization statistics of Church, Ellenberg, and Farb.
ISSN:1073-7928
1687-0247
DOI:10.1093/imrn/rny271