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

Abstract

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.

arXiv admin note: text overlap with arXiv:1712.00071

References in corpus (2)

• Twisted cohomology of configuration spaces and spaces of maximal tori via point-counting
• A trace formula for the distribution of rational $G$-orbits in ramified covers, adapted to representation stability

Cited by in corpus (1)

• Factorization statistics and bug-eyed configuration spaces