Geodesic
Factorization Statistics and the Twisted Grothendieck-Lefschetz formula
Séminaire lotharingien de combinatoire, 80B (2018)
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Factorization statistics are functions defined on the set Polyd(Fq) of all monic degree d polynomials with coefficients in Fq which only depend on the degrees of the irreducible factors of a polynomial. We show that the expected values of factorization statistics are determined by the representation theoretic structure of the cohomology of point configurations in R3. This twisted Grothendieck-Lefschetz formula for Polyd is analogous to a result of Church, Ellenberg, and Farb for squarefree polynomials. Our proof uses formal power series methods which also lead to a new proof of the Church, Ellenberg, and Farb result circumventing algebraic geometry. 

@article{SLC_2018_80B_a5,
     author = {Trevor Hyde},
     title = {Factorization {Statistics} and the {Twisted} {Grothendieck-Lefschetz} formula},
     journal = {S\'eminaire lotharingien de combinatoire},
     year = {2018},
     volume = {80B},
     url = {http://geodesic.mathdoc.fr/item/SLC_2018_80B_a5/}
}
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AU  - Trevor Hyde
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JO  - Séminaire lotharingien de combinatoire
PY  - 2018
VL  - 80B
UR  - http://geodesic.mathdoc.fr/item/SLC_2018_80B_a5/
ID  - SLC_2018_80B_a5
ER  - 
%0 Journal Article
%A Trevor Hyde
%T Factorization Statistics and the Twisted Grothendieck-Lefschetz formula
%J Séminaire lotharingien de combinatoire
%D 2018
%V 80B
%U http://geodesic.mathdoc.fr/item/SLC_2018_80B_a5/
%F SLC_2018_80B_a5
Trevor Hyde. Factorization Statistics and the Twisted Grothendieck-Lefschetz formula. Séminaire lotharingien de combinatoire, 80B (2018). http://geodesic.mathdoc.fr/item/SLC_2018_80B_a5/