On the Solution Sets of Entire Systems of Word Equations

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dc.contributor.authorSaarela Aleksi
dc.contributor.organizationfi=matematiikka|en=Mathematics|
dc.contributor.organization-code1.2.246.10.2458963.20.41687507875
dc.converis.publication-id179651998
dc.converis.urlhttps://research.utu.fi/converis/portal/Publication/179651998
dc.date.accessioned2025-08-27T22:51:58Z
dc.date.available2025-08-27T22:51:58Z
dc.description.abstract<p>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.<br></p>
dc.format.pagerange261
dc.format.pagerange273
dc.identifier.eisbn978-3-031-33180-0
dc.identifier.isbn978-3-031-33179-4
dc.identifier.issn0302-9743
dc.identifier.jour-issn0302-9743
dc.identifier.olddbid202956
dc.identifier.oldhandle10024/185983
dc.identifier.urihttps://www.utupub.fi/handle/11111/48740
dc.identifier.urlhttps://link.springer.com/chapter/10.1007/978-3-031-33180-0_20
dc.identifier.urnURN:NBN:fi-fe2025082789951
dc.language.isoen
dc.okm.affiliatedauthorSaarela, Aleksi
dc.okm.discipline111 Mathematicsen_GB
dc.okm.discipline111 Matematiikkafi_FI
dc.okm.internationalcopublicationnot an international co-publication
dc.okm.internationalityInternational publication
dc.okm.typeA4 Conference Article
dc.publisher.countrySwitzerlanden_GB
dc.publisher.countrySveitsifi_FI
dc.publisher.country-codeCH
dc.publisher.placeCham
dc.relation.conferenceInternational Conference on Combinatorics on Words
dc.relation.doi10.1007/978-3-031-33180-0_20
dc.relation.ispartofjournalLecture Notes in Computer Science
dc.relation.ispartofseriesLecture Notes in Computer Science
dc.relation.volume13899
dc.source.identifierhttps://www.utupub.fi/handle/10024/185983
dc.titleOn the Solution Sets of Entire Systems of Word Equations
dc.title.bookCombinatorics on Words: 14th International Conference, WORDS 2023, Umeå, Sweden, June 12–16, 2023, Proceedings
dc.year.issued2023

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