Orbit-blocking words in free groups

Published 1 May 2025 in math.GR and cs.CC | (2505.00477v1)

Abstract: By strengthening known results about primitivity-blocking words in free groups, we prove that for any nontrivial 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 Whitehead's problem.

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