A4 Refereed article in a conference publication
On the Solution Sets of Entire Systems of Word Equations
Authors: Saarela Aleksi
Editors: Anna Frid, Robert Mercaş
Conference name: International Conference on Combinatorics on Words
Publishing 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
Series title: Lecture Notes in Computer Science
Volume: 13899
First page : 261
Last page: 273
ISBN: 978-3-031-33179-4
eISBN: 978-3-031-33180-0
ISSN: 0302-9743
eISSN: 1611-3349
DOI: https://doi.org/10.1007/978-3-031-33180-0_20
Web address : 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.
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