Random Polynomials over Finite Fields: Statistics and Algorithms

Polynomials appear in many research articles of Philippe Flajolet. Here we concentrate only in papers where polynomials play a crucial role. These involve his studies of the shape of random polynomials over finite fields, the use of these results in the analysis of algorithms for the factorization of polynomials over finite fields, and the relation between the decomposition into irreducibles of a polynomial over a finite field and the general combinatorial decomposition of objects into components. We also comment on a result about the number of real roots of certain family of polynomials of interest in numerical analysis.