Word Equations Where a Power Equals a Product of Powers

Author Aleksi Saarela

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Aleksi Saarela

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Aleksi Saarela. Word Equations Where a Power Equals a Product of Powers. In 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 66, pp. 55:1-55:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


We solve a long-standing open problem on word equations by proving that if the words x_0, ..., x_n satisfy the equation x_0^k = x_1^k ... x_n^k for three positive values of k, then the words commute. One of our methods is to assign numerical values for the letters, and then study the sums of the letters of words and their prefixes. We also give a geometric interpretation of our methods.
  • Combinatorics on words
  • Word equations


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