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math.RA2025
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…
math.RA2023
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…
math.RA2023
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…