Title: A Galois counting problem
Abstract: We count monic cubic and quartic polynomials with prescribed Galois group. We obtain the order of magnitude for quartics, and show that if then irreducible non-polynomials of degree are less prevalent than reducible polynomials of degree . The latter confirms the cubic and quartic cases of a 1936 conjecture of van der Waerden. Joint work with Rainer Dietmann.