A generating function approach to counting theorems for square-free polynomials and maximal tori
arXiv:1410.3540
Abstract
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.
13 pages