A generating function approach to counting theorems for square-free   polynomials and maximal tori
  A recent paper of Church, Ellenberg, and Farb uses topology and representation theory of the symmetric group to prove enumerative results about square-free polynomials and F-stable maximal tori of the general linear group over the algebraic closure of F_q. In this note, we use generating functions to give elementary proofs of some of their results, and some extensions. 
Jason Fulman
math.CO math.AT math.RT