On the Number of Distinct Functional Graphs of Affine-Linear Transformations over Finite Fields
Number Theory
2013-02-20 v2
Abstract
We study the number of non-isomorphic functional graphs of affine-linear transformations from (\F_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 S_{q^n} that intersect AGL_n(q).
Keywords
Cite
@article{arxiv.1208.3229,
title = {On the Number of Distinct Functional Graphs of Affine-Linear Transformations over Finite Fields},
author = {Eric Bach and Andrew Bridy},
journal= {arXiv preprint arXiv:1208.3229},
year = {2013}
}
Comments
10 pages