Vertaisarvioitu artikkeli konferenssijulkaisussa (A4)
On the Solution Sets of Entire Systems of Word Equations
Julkaisun tekijät: Saarela Aleksi
Toimittaja: Anna Frid, Robert Mercaş
Konferenssin vakiintunut nimi: International Conference on Combinatorics on Words
Paikka: Cham
Julkaisuvuosi: 2023
Journal: Lecture Notes in Computer Science
Kirjan nimi *: Combinatorics on Words: 14th International Conference, WORDS 2023, Umeå, Sweden, June 12–16, 2023, Proceedings
Sarjan nimi: Lecture Notes in Computer Science
Volyymi: 13899
Aloitussivu: 261
Lopetussivun numero: 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
Verkko-osoite: https://link.springer.com/chapter/10.1007/978-3-031-33180-0_20
Rinnakkaistallenteen osoite: 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.
