Tutte seminar - Joachim von zur Gathen

Census of polynomials

Abstract:

How many reducible polynomials are there over a finite field? How many squareful ones? Decomposable? Our census looks at such minority polynomials, both multivariate and, for decomposable ones, univariate. Exact results are usually possible but too complicated to be informative. We aim for concise statistical results with rapidly decaying relative error bounds. 

Joint work with Mark Giesbrecht, Alfredo Viola, and Konstantin Ziegler.