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

2014/10/13 by Jason Fulman, Fulman, Jason
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals #Representation Theory (math.RT) #math.AT #math.CO #math.RT

paper · pdf · doi:10.48550/arxiv.1410.3540

13 pages

openalex publication_date 2014/10/13 · arxiv created 2014/10/14 · arxiv updated 2014/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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