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Tropical representations and identities of the stylic monoid

2023-02Artigo científico Acesso aberto
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dc.contributor.authorAird, Thomas
dc.contributor.authorRibeiro, Duarte
dc.contributor.institutionDM - Departamento de Matemática
dc.contributor.institutionCMA - Centro de Matemática e Aplicações
dc.contributor.pblSpringer
dc.date.accessioned2023-07-13T22:18:23Z
dc.date.available2023-07-13T22:18:23Z
dc.date.issued2023-02
dc.descriptionPublisher Copyright: © 2022, The Author(s).
dc.description.abstractWe exhibit a faithful representation of the stylic monoid of every finite rank as a monoid of upper unitriangular matrices over the tropical semiring. Thus, we show that the stylic monoid of finite rank n generates the pseudovariety Jn, which corresponds to the class of all piecewise testable languages of height n, in the framework of Eilenberg’s correspondence. From this, we obtain the equational theory of the stylic monoids of finite rank, show that they are finitely based if and only if n≤ 3 , and that their identity checking problem is decidable in linearithmic time. We also establish connections between the stylic monoids and other plactic-like monoids, and solve the finite basis problem for the stylic monoid with involution.en
dc.description.versionpublishersversion
dc.description.versionpublished
dc.format.extent23
dc.format.extent410741
dc.identifier.doi10.1007/s00233-022-10328-9
dc.identifier.issn0037-1912
dc.identifier.otherPURE: 66129610
dc.identifier.otherPURE UUID: 4af1b4da-6d6f-44e4-abc6-4ebf5e175383
dc.identifier.otherScopus: 85143392135
dc.identifier.otherWOS: 000894573900002
dc.identifier.otherORCID: /0000-0002-6882-8651/work/151373176
dc.identifier.urihttp://hdl.handle.net/10362/155249
dc.identifier.urlhttps://www.scopus.com/pages/publications/85143392135
dc.language.isoeng
dc.peerreviewedyes
dc.relationFunding Information: info:eu-repo/grantAgreement/FCT/3599-PPCDT/PTDC%2FMAT-PUR%2F31174%2F2017/PT
dc.relationinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F04621%2F2020/PT
dc.relationCenter for Computational and Stochastic Mathematics
dc.relationCenter for Computational and Stochastic Mathematics
dc.relationCenter for Mathematics and Applications
dc.relationCenter for Mathematics and Applications
dc.relationinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDP%2F00297%2F2020/PT
dc.subjectFinite basis problem
dc.subjectInvolution
dc.subjectMonoid identities
dc.subjectStylic monoid
dc.subjectTropical representation
dc.subjectUnitriangular matrices
dc.subjectAlgebra and Number Theory
dc.titleTropical representations and identities of the stylic monoiden
dc.typejournal article
degois.publication.firstPage1
degois.publication.issue1
degois.publication.lastPage23
degois.publication.titleSemigroup Forum
degois.publication.volume106
dspace.entity.typePublication
oaire.awardNumberUIDB/04621/2020
oaire.awardNumberUIDP/04621/2020
oaire.awardNumberUIDB/00297/2020
oaire.awardNumberUIDP/00297/2020
oaire.awardTitleCenter for Computational and Stochastic Mathematics
oaire.awardTitleCenter for Computational and Stochastic Mathematics
oaire.awardTitleCenter for Mathematics and Applications
oaire.awardTitleCenter for Mathematics and Applications
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F04621%2F2020/PT
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDP%2F04621%2F2020/PT
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F00297%2F2020/PT
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDP%2F00297%2F2020/PT
oaire.fundingStream6817 - DCRRNI ID
oaire.fundingStream6817 - DCRRNI ID
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oaire.fundingStream6817 - DCRRNI ID
project.funder.identifierhttp://doi.org/10.13039/501100001871
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project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.nameFundação para a Ciência e a Tecnologia
project.funder.nameFundação para a Ciência e a Tecnologia
project.funder.nameFundação para a Ciência e a Tecnologia
project.funder.nameFundação para a Ciência e a Tecnologia
rcaap.rightsopenAccess
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