Representations and identities of plactic-like monoids
Publisher Copyright: © 2022 We exhibit faithful representations of the hypoplactic, stalactic, taiga, sylvester, Baxter and right patience sorting monoids of each finite rank as monoids of upper triangular matrices over any semiring from a large class including the tropical semiring and fields of ch...
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Online Access: | http://hdl.handle.net/10362/145310 https://doi.org/10.1016/j.jalgebra.2022.04.033 |
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ftnewulisboa:oai:run.unl.pt:10362/145310 2023-05-15T18:30:17+02:00 Representations and identities of plactic-like monoids Cain, Alan J. Johnson, Marianne Kambites, Mark Malheiro, António CMA - Centro de Matemática e Aplicações DM - Departamento de Matemática 2022-09-15 32 http://hdl.handle.net/10362/145310 https://doi.org/10.1016/j.jalgebra.2022.04.033 eng eng Funding Information: info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F00297%2F2020/PT info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDP%2F00297%2F2020/PT info:eu-repo/grantAgreement/FCT/3599-PPCDT/PTDC%2FMAT-PUR%2F31174%2F2017/PT 0021-8693 PURE: 44857312 PURE UUID: 4b181318-d7b7-4459-8218-942821b74650 Scopus: 85131355615 WOS: 000832880600016 ORCID: /0000-0003-1186-6216/work/122412291 http://hdl.handle.net/10362/145310 https://doi.org/10.1016/j.jalgebra.2022.04.033 openAccess Baxter monoid Hypoplactic monoid Plactic monoid Representation Semigroup identity Stalactic monoid Sylvester monoid Taiga monoid Tropical semiring Upper triangular matrix semigroup Varieties Algebra and Number Theory article 2022 ftnewulisboa https://doi.org/10.1016/j.jalgebra.2022.04.033 2022-11-23T01:04:38Z Publisher Copyright: © 2022 We exhibit faithful representations of the hypoplactic, stalactic, taiga, sylvester, Baxter and right patience sorting monoids of each finite rank as monoids of upper triangular matrices over any semiring from a large class including the tropical semiring and fields of characteristic 0. By analysing the image of these representations, we show that the variety generated by a single hypoplactic (respectively, stalactic or taiga) monoid of rank at least 2 coincides with the variety generated by the natural numbers together with a fixed finite monoid H (respectively, F) and forms a proper subvariety of the variety generated by the plactic monoid of rank 2. publishersversion published Article in Journal/Newspaper taiga Repositório da Universidade Nova de Lisboa (UNL) Baxter ENVELOPE(162.533,162.533,-74.367,-74.367) Patience ENVELOPE(-68.933,-68.933,-67.750,-67.750) Journal of Algebra 606 819 850 |
institution |
Open Polar |
collection |
Repositório da Universidade Nova de Lisboa (UNL) |
op_collection_id |
ftnewulisboa |
language |
English |
topic |
Baxter monoid Hypoplactic monoid Plactic monoid Representation Semigroup identity Stalactic monoid Sylvester monoid Taiga monoid Tropical semiring Upper triangular matrix semigroup Varieties Algebra and Number Theory |
spellingShingle |
Baxter monoid Hypoplactic monoid Plactic monoid Representation Semigroup identity Stalactic monoid Sylvester monoid Taiga monoid Tropical semiring Upper triangular matrix semigroup Varieties Algebra and Number Theory Cain, Alan J. Johnson, Marianne Kambites, Mark Malheiro, António Representations and identities of plactic-like monoids |
topic_facet |
Baxter monoid Hypoplactic monoid Plactic monoid Representation Semigroup identity Stalactic monoid Sylvester monoid Taiga monoid Tropical semiring Upper triangular matrix semigroup Varieties Algebra and Number Theory |
description |
Publisher Copyright: © 2022 We exhibit faithful representations of the hypoplactic, stalactic, taiga, sylvester, Baxter and right patience sorting monoids of each finite rank as monoids of upper triangular matrices over any semiring from a large class including the tropical semiring and fields of characteristic 0. By analysing the image of these representations, we show that the variety generated by a single hypoplactic (respectively, stalactic or taiga) monoid of rank at least 2 coincides with the variety generated by the natural numbers together with a fixed finite monoid H (respectively, F) and forms a proper subvariety of the variety generated by the plactic monoid of rank 2. publishersversion published |
author2 |
CMA - Centro de Matemática e Aplicações DM - Departamento de Matemática |
format |
Article in Journal/Newspaper |
author |
Cain, Alan J. Johnson, Marianne Kambites, Mark Malheiro, António |
author_facet |
Cain, Alan J. Johnson, Marianne Kambites, Mark Malheiro, António |
author_sort |
Cain, Alan J. |
title |
Representations and identities of plactic-like monoids |
title_short |
Representations and identities of plactic-like monoids |
title_full |
Representations and identities of plactic-like monoids |
title_fullStr |
Representations and identities of plactic-like monoids |
title_full_unstemmed |
Representations and identities of plactic-like monoids |
title_sort |
representations and identities of plactic-like monoids |
publishDate |
2022 |
url |
http://hdl.handle.net/10362/145310 https://doi.org/10.1016/j.jalgebra.2022.04.033 |
long_lat |
ENVELOPE(162.533,162.533,-74.367,-74.367) ENVELOPE(-68.933,-68.933,-67.750,-67.750) |
geographic |
Baxter Patience |
geographic_facet |
Baxter Patience |
genre |
taiga |
genre_facet |
taiga |
op_relation |
Funding Information: info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F00297%2F2020/PT info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDP%2F00297%2F2020/PT info:eu-repo/grantAgreement/FCT/3599-PPCDT/PTDC%2FMAT-PUR%2F31174%2F2017/PT 0021-8693 PURE: 44857312 PURE UUID: 4b181318-d7b7-4459-8218-942821b74650 Scopus: 85131355615 WOS: 000832880600016 ORCID: /0000-0003-1186-6216/work/122412291 http://hdl.handle.net/10362/145310 https://doi.org/10.1016/j.jalgebra.2022.04.033 |
op_rights |
openAccess |
op_doi |
https://doi.org/10.1016/j.jalgebra.2022.04.033 |
container_title |
Journal of Algebra |
container_volume |
606 |
container_start_page |
819 |
op_container_end_page |
850 |
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1766213775192489984 |