The Equation x^i = y^j z^k in a Free Semigroup.

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Harju, Tero and Nowotka, Dirk (2004) The Equation x^i = y^j z^k in a Free Semigroup. Semigroup Forum, 68 (3). pp. 488-490. DOI 10.1007/s00233-003-0028-6.

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Abstract

The equation x^i = y^j z^k 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.

Document Type: Article
Keywords: combinatorics on words free semigroup word equations
Research affiliation: Kiel University
Refereed: Yes
Date Deposited: 12 Feb 2013 16:47
Last Modified: 24 Sep 2019 00:04
URI: https://oceanrep.geomar.de/id/eprint/20293

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