Work

Semigroup identities and varieties of plactic monoids

Year: 2025

Type: article

Abstract: In this paper, we study the semigroup identities satisfied by finite rank plactic monoids. We find a new set of semigroup identities of the plactic monoid of rank n for [Formula: see text], which are shorter than those previously known when [Formula: see text]. Using these semigroup identities we show that for all [Formula: see text], the plactic monoid of rank n satisfies a semigroup identity not satisfied by the semigroup of [Formula: see text] upper triangular tropical matrices. We then prove that the plactic monoid of rank n generates a different semigroup variety for each rank n.

Source: International Journal of Algebra and Computation

DOI: 10.1142/s0218196725500316

Author: Thomas Aird

Institution: University of Manchester

Language: English

Topic: semigroups and automata theory

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4412683056

FWCI: 0.485

Cites: 11

Cited by: 1

Related to: 10