Representations and identities of plactic-like monoids

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 analysi...

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Bibliographic Details
Main Authors: Cain, Alan J., Johnson, Marianne, Kambites, Mark, Malheiro, António
Format: Article in Journal/Newspaper
Language:unknown
Published: arXiv 2021
Subjects:
Rings and Algebras math.RA
Combinatorics math.CO
Group Theory math.GR
FOS Mathematics
20M07, 20M30, 05E99, 12K10, 16Y60
Baxter
Patience
taiga
Online Access:https://dx.doi.org/10.48550/arxiv.2107.04492
https://arxiv.org/abs/2107.04492
id ftdatacite:10.48550/arxiv.2107.04492
record_format openpolar
spelling ftdatacite:10.48550/arxiv.2107.04492 2023-05-15T18:30:23+02:00 Representations and identities of plactic-like monoids Cain, Alan J. Johnson, Marianne Kambites, Mark Malheiro, António 2021 https://dx.doi.org/10.48550/arxiv.2107.04492 https://arxiv.org/abs/2107.04492 unknown arXiv arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ Rings and Algebras math.RA Combinatorics math.CO Group Theory math.GR FOS Mathematics 20M07, 20M30, 05E99, 12K10, 16Y60 Article CreativeWork article Preprint 2021 ftdatacite https://doi.org/10.48550/arxiv.2107.04492 2022-03-10T13:54:43Z 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 $\mathcal{H}$ (respectively, $\mathcal{F}$) forming a proper subvariety of the variety generated by the plactic monoid of rank $2$. : 31 pages Article in Journal/Newspaper taiga DataCite Metadata Store (German National Library of Science and Technology) Baxter ENVELOPE(162.533,162.533,-74.367,-74.367) Patience ENVELOPE(-68.933,-68.933,-67.750,-67.750)
institution Open Polar
collection DataCite Metadata Store (German National Library of Science and Technology)
op_collection_id ftdatacite
language unknown
topic Rings and Algebras math.RA
Combinatorics math.CO
Group Theory math.GR
FOS Mathematics
20M07, 20M30, 05E99, 12K10, 16Y60
spellingShingle Rings and Algebras math.RA
Combinatorics math.CO
Group Theory math.GR
FOS Mathematics
20M07, 20M30, 05E99, 12K10, 16Y60
Cain, Alan J.
Johnson, Marianne
Kambites, Mark
Malheiro, António
Representations and identities of plactic-like monoids
topic_facet Rings and Algebras math.RA
Combinatorics math.CO
Group Theory math.GR
FOS Mathematics
20M07, 20M30, 05E99, 12K10, 16Y60
description 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 $\mathcal{H}$ (respectively, $\mathcal{F}$) forming a proper subvariety of the variety generated by the plactic monoid of rank $2$. : 31 pages
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
publisher arXiv
publishDate 2021
url https://dx.doi.org/10.48550/arxiv.2107.04492
https://arxiv.org/abs/2107.04492
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_rights arXiv.org perpetual, non-exclusive license
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
op_doi https://doi.org/10.48550/arxiv.2107.04492
_version_ 1766213877211594752

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