30 citations · 132 across the 31 of their papers we have counts for
4 papers · 1 filter
Combinatorics of cyclic shifts in plactic, hypoplactic, sylvester, and related monoids
Alan J. Cain, António Malheiro
The cyclic shift graph of a monoid is the graph whose vertices are elements of the monoid and whose edges link elements that differ by a cyclic shift. For certain monoids connected…
Identities in plactic, hypoplactic, sylvester, Baxter, and related monoids
Alan J. Cain, António Malheiro
This paper considers whether non-trivial identities are satisfied by certain `plactic-like' monoids that, like the plactic monoid, are closely connected to combinatorics. New resul…
Crystallizing the hypoplactic monoid: from quasi-Kashiwara operators to the Robinson--Schensted--Knuth-type correspondence for quasi-ribbon tableaux
Alan J. Cain, António Malheiro
Crystal graphs, in the sense of Kashiwara, carry a natural monoid structure given by identifying words labelling vertices that appear in the same position of isomorphic components…
Automaton semigroups: new construction results and examples of non-automaton semigroups
Tara Brough, Alan J. Cain
This paper studies the class of automaton semigroups from two perspectives: closure under constructions, and examples of semigroups that are not automaton semigroups. We prove that…