Automorphic orbits in free groups: recent progress
Group Theory
2025-10-09 v3
Abstract
In this survey, we describe recent progress on asymptotic properties of various automorphic orbits in free groups. In particular, we address the problem of counting potentially positive elements of a given length. We also discuss complexity (worst-case, average-case, and generic-case) of Whitehead's automorphism problem and relevant properties of automorphic orbits, including orbit-blocking words.
Cite
@article{arxiv.2510.00889,
title = {Automorphic orbits in free groups: recent progress},
author = {Vladimir Shpilrain},
journal= {arXiv preprint arXiv:2510.00889},
year = {2025}
}
Comments
8 pages