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arXiv · 2510.00889

Automorphic orbits in free groups: recent progress

Vladimir Shpilrain
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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.

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Vladimir Shpilrain. 2025-10-01. Automorphic orbits in free groups: recent progress. https://doi.org/10.46298/jgcc.2026.18.1.16639

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