Refereed article in conference proceedings (A4)

On the Solution Sets of Entire Systems of Word Equations

List of AuthorsSaarela Aleksi

EditorsAnna Frid, Robert Mercaş

Conference nameInternational Conference on Combinatorics on Words


Publication year2023

JournalLecture Notes in Computer Science

Book title *Combinatorics on Words: 14th International Conference, WORDS 2023, Umeå, Sweden, June 12–16, 2023, Proceedings

Title of seriesLecture Notes in Computer Science

Volume number13899

Start page261

End page273







Self-archived copy’s web address


The set of all constant-free word equations satisfied by a given morphism is called an entire system of equations. We show that in the three-variable case, the set of nonperiodic solutions of any entire system can be described using parametric formulas with just one numerical parameter. We also show how the solution set of any equation can be represented as a union of solution sets of entire systems. Even though an infinite union is needed in some cases, this still points towards a stronger version of Hmelevskii’s theorem about parametric solutions of three-variable word equations.

Last updated on 2023-02-08 at 09:17