António Malheiro
Associate Professor w/ habilitation, Mathematics Department
Faculdade de Ciências e Tecnologia UNL, Monte da Caparica, 2829-516 Caparica, Tel: (+351) 212948388 ext. 10832 (email)
A note on identities in plactic monoids and monoids of upper-triangular tropical matrices
- Citation:
- Cain, A. J., G. Klein, Ł. Kubat, A. Malheiro, and J. Okniński A note on identities in plactic monoids and monoids of upper-triangular tropical matrices. ArXiv e-prints., 2017.
Abstract:
This paper uses the combinatorics of Young tableaux to prove the plactic monoid of infinite rank does not satisfy a non-trivial identity, by showing that the plactic monoid of rank n cannot satisfy a non-trivial identity of length less than or equal to n. A new identity is then proven to hold for the monoid of n×n upper-triangular tropical matrices. Finally, a straightforward embedding is exhibited of the plactic monoid of rank 3 into the direct product of two copies of the monoid of 3×3 upper-triangular tropical matrices, giving a new proof that the plactic monoid of rank 3 satisfies a non-trivial identity.
Notes:
n/a
