Polynomial factorization statistics and point configurations in $\mathbb{R}^3$

30 Jan 2018 Hyde Trevor

We use generating functions 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 methods lead to a new proof of the twisted Grothendieck-Lefschetz formula for squarefree polynomial factorization statistics of Church, Ellenberg, and Farb...

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Categories


  • REPRESENTATION THEORY
  • COMBINATORICS
  • NUMBER THEORY