Refereed article in conference proceedings (A4)

On the Solution Sets of Entire Systems of Word Equations

List of Authors: Saarela Aleksi

Editors: Anna Frid, Robert Mercaş

Conference name: International Conference on Combinatorics on Words

Place: Cham

Publication year: 2023

Journal: Lecture Notes in Computer Science

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

Title of series: Lecture Notes in Computer Science

Volume number: 13899

Start page: 261

End page: 273

ISBN: 978-3-031-33179-4

eISBN: 978-3-031-33180-0

ISSN: 0302-9743

eISSN: 1611-3349

DOI: http://dx.doi.org/10.1007/978-3-031-33180-0_20

URL: https://link.springer.com/chapter/10.1007/978-3-031-33180-0_20

Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/179651998

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.