Tropical representations and identities of the stylic monoid
Autor(a) principal: | |
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Data de Publicação: | 2023 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10362/155249 |
Resumo: | Publisher Copyright: © 2022, The Author(s). |
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Tropical representations and identities of the stylic monoidFinite basis problemInvolutionMonoid identitiesStylic monoidTropical representationUnitriangular matricesAlgebra and Number TheoryPublisher Copyright: © 2022, The Author(s).We 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.DM - Departamento de MatemáticaCMA - Centro de Matemática e AplicaçõesRUNAird, ThomasRibeiro, Duarte2023-07-13T22:18:23Z2023-022023-02-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article23application/pdfhttp://hdl.handle.net/10362/155249eng0037-1912PURE: 66129610https://doi.org/10.1007/s00233-022-10328-9info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-03-11T05:37:47Zoai:run.unl.pt:10362/155249Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:55:59.749289Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Tropical representations and identities of the stylic monoid |
title |
Tropical representations and identities of the stylic monoid |
spellingShingle |
Tropical representations and identities of the stylic monoid Aird, Thomas Finite basis problem Involution Monoid identities Stylic monoid Tropical representation Unitriangular matrices Algebra and Number Theory |
title_short |
Tropical representations and identities of the stylic monoid |
title_full |
Tropical representations and identities of the stylic monoid |
title_fullStr |
Tropical representations and identities of the stylic monoid |
title_full_unstemmed |
Tropical representations and identities of the stylic monoid |
title_sort |
Tropical representations and identities of the stylic monoid |
author |
Aird, Thomas |
author_facet |
Aird, Thomas Ribeiro, Duarte |
author_role |
author |
author2 |
Ribeiro, Duarte |
author2_role |
author |
dc.contributor.none.fl_str_mv |
DM - Departamento de Matemática CMA - Centro de Matemática e Aplicações RUN |
dc.contributor.author.fl_str_mv |
Aird, Thomas Ribeiro, Duarte |
dc.subject.por.fl_str_mv |
Finite basis problem Involution Monoid identities Stylic monoid Tropical representation Unitriangular matrices Algebra and Number Theory |
topic |
Finite basis problem Involution Monoid identities Stylic monoid Tropical representation Unitriangular matrices Algebra and Number Theory |
description |
Publisher Copyright: © 2022, The Author(s). |
publishDate |
2023 |
dc.date.none.fl_str_mv |
2023-07-13T22:18:23Z 2023-02 2023-02-01T00:00:00Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10362/155249 |
url |
http://hdl.handle.net/10362/155249 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
0037-1912 PURE: 66129610 https://doi.org/10.1007/s00233-022-10328-9 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
23 application/pdf |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799138145925595136 |