5 papers
Growth and identities of monogenic free adequate monoids
Thomas Aird, Daniel Heath
Motivated by recent advances in inverse semigroup theory, we investigate the growth of and identities satisfied by free left and free two-sided adequate monoids. We explicitly comp…
The Schützenberger groups and maximal subgroups of tropical matrices
Thomas Aird
We classify the Schützenberger groups of the category of matrices over the tropical semiring, , in doing so, we obtain a classification for the Schützenberger groups…
Short presentations for transformation monoids
Thomas Aird, James D. Mitchell, Murray T. Whyte
By the theorems of Cayley and Vagner-Preston, the full transformation monoids and the symmetric inverse monoids play analogous roles in the theory of monoids and inverse monoids, a…
Lattices of varieties of plactic-like monoids
Thomas Aird, Duarte Ribeiro
We study the equational theories and bases of meets and joins of several varieties of plactic-like monoids. Using those results, we construct sublattices of the lattice of varietie…
Plactic-like monoids arising from meets and joins of stalactic and taiga congruences
Thomas Aird, Duarte Ribeiro
We study the four plactic-like monoids that arise by taking the meets and joins of stalactic and taiga congruences. We obtain the combinatorial objects associated with the meet mon…