On the Number of Distinct Functional Graphs of Affine-Linear Transformations over Finite Fields
Abstract
We study the number of non-isomorphic functional graphs of affine-linear transformations from (q)n to itself, and we prove upper and lower bounds on this quantity for n large. As a corollary to our result, we prove bounds on the number of conjugacy classes in the symmetric group Sqn that intersect AGLn(q).
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