30 citations · 132 across the 31 of their papers we have counts for
43 papers
Commutative nilpotent transformation semigroups
Alan J. Cain, António Malheiro, Tânia Paulista
Cameron, et al. determined the maximum size of a null subsemigroup of the full transformation semigroup on a finite set and provided a description of the null…
A local characterization of quasi-crystal graphs
Alan J. Cain, António Malheiro, Fátima Rodrigues +1
It is provided a local characterization of quasi-crystal graphs, by presenting a set of local axioms, similar to the ones introduced by Stembridge for crystal graphs of simply-lace…
Structure of quasi-crystal graphs and applications to the combinatorics of quasi-symmetric functions
Alan J. Cain, António Malheiro, Fátima Rodrigues +1
Crystal graphs are powerful combinatorial tools for working with the plactic monoid and symmetric functions. Quasi-crystal graphs are an analogous concept for the hypoplactic monoi…
Every numerical semigroup arises as an automaton monoid
Tara Macalister Brough, Alan J. Cain, Jan Philipp Wächter
This paper shows how to construct explicitly an automaton that generates an arbitrary numerical semigroup.
Quasi-crystals for arbitrary root systems and associated generalizations of the hypoplactic monoid
Alan J. Cain, Ricardo P. Guilherme, António Malheiro
The hypoplactic monoid was introduced by Krob and Thibon through a presentation and through quasi-ribbon tableaux and an insertion algorithm. Just as Kashiwara crystals enriched th…
Representations and identities of plactic-like monoids
Alan J. Cain, Marianne Johnson, Mark Kambites +1
We exhibit faithful representations of the hypoplactic, stalactic, taiga, sylvester, Baxter and right patience sorting monoids of each finite rank as monoids of upper triangular ma…