On the Number of Distinct Functional Graphs of Affine-Linear\n Transformations over Finite Fields

2012/08/15 by Eric Bach, Bach, Eric, Andrew Bridy +1 · 1 citation
Computer Science · Mathematics · #11T55 (Secondary) #37P05 (Primary) 05C20 #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Graph theory and applications #Limits and Structures in Graph Theory #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1208.3229

openalex publication_date 2012/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the number of non-isomorphic functional graphs of affine-linear\ntransformations from ( F_q)ⁿ to itself, and we prove upper and lower bounds on\nthis quantity for n large. As a corollary to our result, we prove bounds on the\nnumber of conjugacy classes in the symmetric group S_qⁿ that intersect\nAGL_n(q).\n

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