On the number of distinct functional graphs of affine-linear transformations over finite fields

摘要

We study the number of non-isomorphic functional graphs of affine-linear transformations from (~(Fq))~n to itself, and we prove upper and lower bounds on this quantity as n→ ∞. As a corollary to our result, we prove bounds on the number of conjugacy classes in the symmetric group Sqn that intersect AGL_n(q).