Word equations where a power equals a product of powers

: Aleksi Saarela

: Heribert Vollmer, Brigitte Vallée

: Symposium on Theoretical Aspects of Computer Science (STACS)

Publisher: Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

: 2017

: LIPICS – Leibniz international proceedings in informatics

: 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)

: Leibniz International Proceedings in Informatics, LIPIcs

: Leibniz International Proceedings in Informatics (LIPIcs)

: 66

: 9783959770286

: 1868-8969

DOI: https://doi.org/10.4230/LIPIcs.STACS.2017.55(external)

: https://research.utu.fi/converis/portal/detail/Publication/26890766(external)

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.

LIPIcs-STACS-2017-55.pdf