Q-Hit Polynomials Have Only Real Roots

We prove that Garsia and Remmel's q-hit polynomials for Ferrers boards have only real roots for fixed q > 0. This generalizes previous results by Haglund, Wagner and Ono [4] and Savage and Visontai [5]. We also extend the main recursion in [5] to hit polynomials for certain classes of Ferrers boards, which include the multiset Eulerian polynomials.