Research reveals the existence of orbit-blocking words in free groups, indicating implications for average-case complexity.
By strengthening known results about primitivity-blocking words in free groups, we prove that, for any element 𝑤 of a free group of finite rank, there are words that cannot be subwords of any cyclically reduced automorphic image of 𝑤. This has implications for the average-case complexity of a variant of Whitehead’s problem.
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Koch-Hyde et al. (2026) studied this question.
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