A4 Refereed article in a conference publication
Word equations where a power equals a product of powers
Authors: Aleksi Saarela
Editors: Heribert Vollmer, Brigitte Vallée
Conference name: Symposium on Theoretical Aspects of Computer Science (STACS)
Publisher: Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Publication year: 2017
Journal: LIPICS – Leibniz international proceedings in informatics
Book title : 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)
Journal name in source: Leibniz International Proceedings in Informatics, LIPIcs
Series title: Leibniz International Proceedings in Informatics (LIPIcs)
Volume: 66
ISBN: 9783959770286
ISSN: 1868-8969
DOI: https://doi.org/10.4230/LIPIcs.STACS.2017.55
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/26890766
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.
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