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A recent paper of Church, Ellenberg, and Farb uses topology andrepresentation theory of the symmetric group to prove enumerative results aboutsquare-free polynomials and F-stable maximal tori of the general linear groupover the algebraic closure of F_q. In this note, we use generating functions togive elementary proofs of some of their results, and some extensions.

A generating function approach to counting theorems for square-free polynomials and maximal tori