Factorization patterns on nonlinear families of univariate polynomials over a finite field

Guillermo Matera, Mariana Pérez, Melina Privitelli

We estimate the number $|{\mathcal{A}}_{\mathbf{\lambda }}|$ of elements on a nonlinear family $\mathcal{A}$ of monic polynomials of ${\mathbb{F}}_q[T]$ of degree $r$ having factorization p…