An Improved Version of Hmelevskii's Theorem on Three-Variable 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-id526554894
dc.converis.urlhttps://research.utu.fi/converis/portal/Publication/526554894
dc.date.accessioned2026-06-16T20:10:41Z
dc.description.abstract<p>Hmelevskii proved in 1971 that every constant-free three-variable word equation has a parametric solution. We prove an improved version of this result by showing that every such equation has a parametric solution using only three numerical parameters and with only two levels of nesting. This means that the structure of the solution sets of these equations is considerably simpler than has been known before.</p>
dc.identifier.isbn978-3-95977-412-3
dc.identifier.urihttps://www.utupub.fi/handle/11111/62105
dc.identifier.urlhttps://doi.org/10.4230/LIPIcs.STACS.2026.77
dc.identifier.urnURN:NBN:fi-fe2026061672462
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.countryGermanyen_GB
dc.publisher.countrySaksafi_FI
dc.publisher.country-codeDE
dc.relation.conferenceSymposium on Theoretical Aspects of Computer Science
dc.relation.doi10.4230/LIPIcs.STACS.2026.77
dc.relation.ispartofjournalLIPICS – Leibniz International Proceedings in Informatics
dc.relation.volume364
dc.titleAn Improved Version of Hmelevskii's Theorem on Three-Variable Word Equations
dc.title.book43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)
dc.year.issued2026

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