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The Equation xi = yjzk in a Free Semigroup

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Abstract

The equation xi = yjzk has only periodic solutions in a free semigroup. This result was first proven by Lyndon and Schützenberger. We present a very short proof of this classical result. Moreover, we establish that the power of two or more of a primitive word cannot be factorized into conjugates of a different word.

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Authors and Affiliations

  1. Turku Centre of Computer Science (TUCS), Department of Mathematics, University of Turku, Finland

    Tero Harju & Dirk Nowotka

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  1. Tero Harju
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  2. Dirk Nowotka
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Correspondence to Dirk Nowotka.

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Edited by Jean-Eric Pin

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Harju, T., Nowotka, D. The Equation xi = yjzk in a Free Semigroup. Semigroup Forum 68, 488–490 (2004). https://doi.org/10.1007/s00233-003-0028-6

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  • DOI: https://doi.org/10.1007/s00233-003-0028-6

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