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From plactic monoids to hypoplactic monoids
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The plactic monoids can be obtained from the tensor product of crystals. Similarly, the hypoplactic monoids can be obtained from the quasi-tensor product of quasi-crystals. In this paper, we present a unified approach to these constructions by expressing them in the context of quasi-crystals. We provide a sufficient condition to obtain a quasi-crystal monoid for the quasi-tensor product from a quasi-crystal monoid for the tensor product. We also establish a sufficient condition for a hypoplactic monoid to be a quotient of the plactic monoid associated to the same seminormal quasi-crystal.
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Funding Information:
Open access funding provided by FCT|FCCN (b-on). This work is funded by national funds through the FCT– Fundação para a Ciência e a Tecnologia, I.P., under the scope of the projects UIDB/00297/2020 (https://doi.org/10.54499/UIDB/00297/2020) and UIDP/00297/2020 (https://doi.org/ 10.54499/UIDP/00297/2020) (Center for Mathematics and Applications).
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© The Author(s) 2024.
Palavras-chave
Equidivisible Hypoplactic monoid Plactic monoid Quasi-crystal Algebra and Number Theory