From plactic monoids to hypoplactic monoids
Rings and Algebras
2023-11-16 v1 Combinatorics
Group Theory
Abstract
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.
Cite
@article{arxiv.2311.08523,
title = {From plactic monoids to hypoplactic monoids},
author = {Ricardo P. Guilherme},
journal= {arXiv preprint arXiv:2311.08523},
year = {2023}
}
Comments
23 pages. arXiv admin note: substantial text overlap with arXiv:2301.00271