2023/11/14 by Ricardo P. Guilherme, Guilherme, Ricardo P.
Mathematics · #05E16 #20M05 (Secondary) #20M10 (Primary) #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2311.08523
openalex publication_date 2023/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.