1 citations · 1 across the 5 of their papers we have counts for
5 papers
Semigroup identities and varieties of plactic monoids
Thomas Aird
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 for , which are sh…
Tropical Representations and Identities of the Stylic Monoid
Thomas Aird, Duarte Ribeiro
We exhibit a faithful representation of the stylic monoid of every finite rank as a monoid of upper unitriangular matrices over the tropical semiring. Thus, we show that the stylic…
Generating sets, presentations, and growth of tropical matrix monoids
Thomas Aird
We construct minimal and irredundant generating sets for a family of submonoids of the monoid of upper triangular matrices over a commutative semiring. We show that th…
Identities of tropical matrices and plactic monoids
Thomas Aird
We study semigroup varieties generated by full and upper triangular tropical matrix semigroups and the plactic monoid of rank 4. We prove that the upper triangular tropical matrix…
Permutability of Matrices over Bipotent Semirings
Thomas Aird, Mark Kambites
We study permutability properties of matrix semigroups over commutative bipotent semirings (of which the best-known example is the tropical semiring). We prove that every such semi…