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arXiv · 2109.11957

Freeness of Sch\"utzenberger groups of primitive substitutions

Herman Goulet-Ouellet
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Abstract

Our main goal is to study the freeness of Sch\"utzenberger groups defined by primitive substitutions. Our findings include a simple freeness test for these groups, which is applied to exhibit a primitive invertible substitution with corresponding non-free Sch\"utzenberger group. This constitutes a counterexample to a result of Almeida dating back to 2005. We also give some early results concerning relative freeness of Sch\"utzenberger groups, a question which remains largely unexplored.

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Herman Goulet-Ouellet. 2021-09-24. Freeness of Sch\"utzenberger groups of primitive substitutions. https://doi.org/10.1142/s0218196722500473

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