Polynomial Factorization Statistics and Point Configurations in ℝ3

@article{Hyde2018PolynomialFS,
  title={Polynomial Factorization Statistics and Point Configurations in ℝ3},
  author={Trevor Hyde},
  journal={International Mathematics Research Notices},
  year={2018}
}
  • Trevor Hyde
  • Published 30 January 2018
  • Mathematics
  • International Mathematics Research Notices
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. 

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