Abstract

The equation xⁱ = y^jz^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.

Keywords: combinatorics on words, free semigroup, word equations

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