Automorphic orbits in free groups: recent progress
arXiv:2510.00889 · doi:10.46298/jgcc.2026.18.1.16639
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.
8 pages. Published in the journal of Groups, Complexity, Cryptology