Automorphic orbits in free groups: recent progress
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
Authors
- Vladimir Shpilrain (ORCID: https://orcid.org/0000-0003-2239-7996)
Institutions
- City College of New York (US)
Publication Details
- Journal
- journal of Groups complexity cryptology
- Published
- 2026-06-19
- DOI
- https://doi.org/10.46298/jgcc.2026.18.1.16639
- Primary Topic
- Geometric and Algebraic Topology
- Type
- preprint
- Field-Weighted Citation Impact
- 0.00