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

الأصل · EN

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 Fq. In this note, we use generating functions to give elementary proofs of some of their results, and some extensions.