Tropical representations and identities of the stylic monoid

Detalhes bibliográficos
Autor(a) principal: Aird, Thomas
Data de Publicação: 2023
Outros Autores: Ribeiro, Duarte
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).
id RCAP_6cd514e9c2939d21aa590fbd29c38db6
oai_identifier_str oai:run.unl.pt:10362/155249
network_acronym_str RCAP
network_name_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository_id_str 7160
spelling 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
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str 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
repository.mail.fl_str_mv
_version_ 1799138145925595136

Registros relacionados