2026-07-23T03:45:46Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:6979 2024-03-06T10:39:14Z ddc:004 open_access

Word Equations Where a Power Equals a Product of Powers Saarela, Aleksi Combinatorics on words Word equations 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Aleksi Saarela 2017 Is Part Of LIPIcs, Volume 66, 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2017.55 urn:nbn:de:0030-drops-69793 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2017.55 eng https://creativecommons.org/licenses/by/3.0/legalcode