# 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} }

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.

## 6 Citations

### Factorization statistics and the twisted Grothendieck-Lefschetz formula

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- 2017

We announce recent results on a connection between factorization statistics of polynomials over a finite field and the structure of the cohomology of configurations in $\mathbb{R}^3$ as a…

### Configuration spaces on a wedge of spheres and Hochschild-Pirashvili homology

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### Liminal reciprocity and factorization statistics

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Let $M_{d,n}(q)$ denote the number of monic irreducible polynomials in $\mathbb{F}_q[x_1, x_2, \ldots , x_n]$ of degree $d$. We show that for a fixed degree $d$, the sequence $M_{d,n}(q)$ converges…

### Eulerian representations for real reflection groups

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The Eulerian idempotents, first introduced for the symmetric group and later extended to all reflection groups, generate a family of representations called the Eulerian representations that decompose…

### Cyclotomic factors of necklace polynomials

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Necklace polynomials $M_d(x)$ play an important role in number theory, combinatorics, dynamics, and representation theory. In this paper we introduce and analyze the \emph{cyclotomic factor…

### Factorization statistics and bug-eyed configuration spaces

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A recent theorem of Hyde proves that the factorizations statistics of a random polynomial over a finite field are governed by the action of the symmetric group on the configuration space of $n$…

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